Trigonometry

Problem 801

Write the expression in terms of first powers of cosine. Do not use decimals in your answer. Make sure to simplify as much as possible. $\sin ^{4} x=$ $\square$
$\cos$ $\square$

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Problem 802

Let $\sin A=\frac{3}{5}$ with $A$ in QII and $\sin B=-\frac{8}{17}$ with $B$ in QIII. Find $\sin (A+B), \cos (A+B)$ , and $\tan (A+B)$ . $\begin{array}{l} \sin (A+B)=\square \\ \cos (A+B)=\square \\ \tan (A+B)=\square \end{array}$
In what quadrant does $A+B$ terminate? quadrant I quadrant II quadrant III quadrant IV Submit Answer

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Problem 803

Solve the equation. Write the numbers using integers or simplified fractions. $\sec (-2 x)=-\sqrt{2}$
Part: $0 / 2$
Part 1 of 2 (a) Write the solution set for the general solution. Use $n_{j}$ where $n$ is an integer.
The solution set for the general solution is $\{x \mid x=$ $\square$ $x=$ $\square$ 1\}. $\square$

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Problem 804

Solve the equation on the interval $[0,2 \pi)$ . Give the exact solution in radians and give an approximation in degrees rounded to 1 decimal place. $\cos x=\frac{1}{6}$
Part: 0 / 2
Part 1 of 2
The exact solution set in radians is $\square$ \}.
Write your answer in simplest form.

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Problem 805

$\text{Traccia il grafico della funzione } y = 2 \sin \left(x + \frac{5 \pi}{6}\right) - 1 \text{ e individua i punti di massimo e di minimo.}$

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Problem 806

Statement Rule $\left(\csc ^{2} x-1\right) \sec ^{2} x$ $=\cot ^{2} x \sec ^{2} x$
Rule? $=\left(\frac{\cos ^{2} x}{\sin ^{2} x}\right) \sec ^{2} x$ Rule? $=\left(\frac{\cos ^{2} x}{\sin ^{2} x}\right)\left(\frac{1}{\cos ^{2} x}\right)$ Rule? $=\frac{1}{\sin ^{2} x}$ Rule? $=\csc ^{2} x$ Rule?

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Problem 807

Find the reference angle for $\frac{41 \pi}{12}$ .

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Problem 808

Let $\theta$ be an angle in quadrant IV such that $\csc \theta=-\frac{5}{3}$ . Find the exact values of $\tan \theta$ and $\cos \theta$ . $\tan \theta=$ $\square$ $\cos \theta=$ $\square$

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Problem 809

If $\theta=240^{\circ}$ , find the exact value of each expression below. (a) $2 \cos \theta=$ $\square$ (b) $\quad \cos \frac{\theta}{2}=$ $\square$ (c) $\cos ^{2} \theta=$ $\square$

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Problem 810

$\text{Given } \theta = -675^\circ, \text{ find the following:}$ \begin{enumerate} \item[(b)] \text{Find an angle between } 0^\circ \text{ and } 360^\circ \text{ that is coterminal with } \theta. \item[(c)] \text{Find an angle between } -360^\circ \text{ and } 0^\circ \text{ that is coterminal with } \theta. \end{enumerate}

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Problem 811

The unit circle is shown below. Complete the following. (a) Sketch $\theta=-30^{\circ}$ in standard position on the unit circle.
Find the lengths of the legs of its reference triangle. These are labeled $a$ and $b$ in the figure below, when an angle is sketched. Then use your reference triangle to find the coordinates of point $P$ . Use exact values and not decimal approximations. $\begin{array}{l} a=\square \\ b=\square \\ P=(\square, \square) \end{array}$

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Problem 812

40- Two vectors have magnitudes of 10 m and 15 m . The angle between them when they are drawn with their tails at the same point is $65^{\circ}$ . The component of the longer vector along the line of the shorter is: A. 0 B. 4.2 m C. 6.3 m D. 9.1 m E. 14 m

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Problem 813

E.g. Solve the following triangles: a. b. $\begin{array}{l} \angle P=180^{\circ}-90^{\circ}-37^{\circ}=53^{\circ} \\ \cos 37^{\circ}-1 \frac{19}{q} \\ \tan 37^{\circ}=\frac{r}{19} \\ q=\frac{19}{\cos 37^{\circ}} \\ r=19 \tan 37^{\circ} \\ q \doteq 23.8 \\ r \doteq 14.3 \end{array}$ $\therefore \angle P=53^{\circ}, q \doteq 23.8 \mathrm{~cm}, r \equiv 19.3 \mathrm{~cm}$

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Problem 814

$5 \sin x \cos x+\cos x=0$

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Problem 815

Solve $\cos ^{2}(x)=-8 \sin (x)$ for all solutions $0 \leq x<2 \pi$ . $x=$

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Problem 816

Convert the angle $\frac{3 \pi}{5}$ from radians to degrees.

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Problem 817

Find the exact value of $\cos \frac{2 \pi}{9} \cos \frac{\pi}{18}+\sin \frac{2 \pi}{9} \sin \frac{\pi}{18}$

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Problem 818

Sketch an angle $\theta$ with the point $(-6,0)$ on its terminal side. Find the six trig functions of $\theta$ .

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Problem 819

Determine if $\sin \left[(4 n+3) \cdot 90^{\circ}\right]$ equals 0, 1, -1, or is undefined for integer $n$ .

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Problem 820

Determine if the ratio $\frac{y}{r}$ is positive or negative for the point $(x, y)$ in quadrant II, where $r=\sqrt{x^{2}+y^{2}}$ .

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Problem 821

Find the value of $\cos(0^{\circ})$ .

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Problem 822

Find the value of $\sec 180^{\circ}$ .

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Problem 823

Find the value of $\tan 900^{\circ}$ .

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Problem 824

Find the value of $\cos 1800^{\circ}$ .

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Problem 825

Find the value of $\csc 3150^{\circ}$ .

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Problem 826

Trova il periodo della funzione $y=\sin \frac{2}{3} x$ .

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Problem 827

Determine the period of the function $y=2 \cos 2x + \sin x$ .

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Problem 828

Note: Triangle may not be drawn to scale. Suppose $\mathrm{c}=9$ and $\mathrm{A}=35$ degrees. Find: $a=$ $b=$ $B=$ $\square$ degrees

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Problem 829

Solve for $x$ . Round to the nearest tenth, if necessary.

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Problem 830

$\tan ^{2}(\theta)-1=0$

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Problem 831

$2 \cos ^{2}(\theta)-\cos (\theta)-1=0$

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Problem 832

Determine the specific solutions (if any) on the interval $[0,2 \pi$ ). $\tan \theta+\sqrt{3}=0$
Select the correct choice below and, if necessary, fill in the answer box withit A. $\theta=$ $\square$ (Use a comma to separate answers as needed. Simplify your answer B. There is no solution.

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Problem 833

anie Dads.
Question Watch Video
Find an angle $\theta$ coterminal to $1163^{\circ}$ , where $0^{\circ} \leq \theta<360^{\circ}$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 834

Question Watch Video Show Examples
For the rotation $-297^{\circ}$ , find the coterminal angle from $0^{\circ} \leq \theta<360^{\circ}$ , the quadrant, and the reference angle.
Answer Attempt 1 out of 2
The coterminal angle is of $\square$ ${ }^{\circ}$ 。 $\square$ ${ }^{\circ}$ , which lies in Quadrant Submit Answer

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Problem 835

The Washington Monument is 555 ft tall. The angle of elevation from the end of the monument's shadow to the top of the monument has a cosecant of 1.10. a. $\theta=$ $\square$ (Type your answer in degrees. Rou

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Problem 836

Show Examples
The terminal ray of an angle $\theta$ intersects the unit circle as shown below. Use the given coordinates to calculate $\cos \theta$ rounded to three decimal places, if necessary. Answer Attempt 1 put of 2

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Problem 837

Chapter 8: Graphs of Trigonomeulic 350 [EX4] A ferris wheel with a diameter of 32 m makes 2 revolutions every 10 minutes. The center of the wheel is 18 m above the ground. Suppose Philip gets on an ascending car, 18 m above the ground at time $t=0$ . (1) Draw a graph to show how Philip's position ( $h$ ) above the ground varies with time ( $t$ ) for the first revolution.

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Problem 838

$1+\frac{1}{\tan ^{2} x}=\frac{1}{\sin ^{2} x}$

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Problem 839

Here is a little more review concerning trig functions. Using the formula for $\sin ()$ and $\cos ()$ of the sum of two angles. $\begin{array}{ll} 3 \cos (5 x-2)=3 \cos (2) & \cos (5 x)- \\ 3 \sin (2 x-2)=-3 \sin (2) & \cos (2 x)+3 \cos (2) \end{array}$
Now reverse this formula and given the expanded version find the version with just one term. This involves solving a pair of equations -in order to get $A \cos (x)+B \sin (x)=R \sin (x+b)=R \sin (b) \cos (x)+R \cos (b) \sin (x)$ what values must you choose for $R$ and $b$ ? (Match coefficients.)
By convention we'll assume that the amplitude (the first coefficient on the left hand side) is positive. $\begin{array}{l} \cos (5 x+\square)=4 \cos (5 x)+-2 \sin (5 x) \\ \sin (2 x+\arctan (3) \quad \text { - })=6 \cos (2 x)+2 \sin (2 x) \end{array}$
The upshot of this exercise is that we can always rewrite the sum of multiples of $\sin ()$ and $\cos ()$ as a $\operatorname{single} \sin ()$ function with a given amplitude and phase shift. We could also write it as a single $\cos ()$ , but it would have a different phase in that case. We'll use this many times in interpreting results.

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Problem 840

Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (inc answer.
What signs are $\cos \left(-140^{\circ}\right)$ and $\tan \left(-140^{\circ}\right)$ ? $\cos \left(-140^{\circ}\right)>0$ and $\tan \left(-140^{\circ}\right)<0$ $\cos \left(-140^{\circ}\right)<0$ and $\tan \left(-140^{\circ}\right)>0$ They are both negative. They are both positive. Submit Pass Don't know answer

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Problem 841

Evaluate each expression. (a) $\sin x$ if $x=\left(\frac{1}{4}\right)^{\circ}$
Round your answer to four decimal places. (b) $\sin ^{-1} x$ if $x=\frac{1}{4}$
Round your answer to three decimal places. (c) $(\sin x)^{-1}$ if $x=\left(\frac{1}{4}\right)^{\circ}$
Round your answer to three decimal places.

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Problem 842

Explain what each of the following expressions means. Evaluate each expression for $x=0.5$ . NOTE: Give the exact answer in radians, or round to three decimal places. (a) $\sin ^{-1}(x)$ is $\square$ $\sin ^{-1}(x)=$ $\square$ (b) $\sin x^{-1}$ is $\square$ $\sin \left(x^{-1}\right)=$ $\square$ (c) $(\sin (x))^{-1}$ is $\square$ $(\sin (x))^{-1}=$ $\square$

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Problem 843

Evaluate each expression. (a) $\sin x+\cos x+\tan x$ if $x=45^{\circ}$
NOTE: Enter the exact answer. (b) $(\sin x)^{-1}+(\cos x)^{-1}+(\tan x)^{-1}$ if $x=45^{\circ}$
NOTE: Enter the exact answer. $\square$ (c) $\sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x$ if $x=0.45$ NOTE: Round your answer to three decimal places. $\square$

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Problem 844

Evaluate without using a calculator. NOTE: If the answer is undefined, indicate that using the check box. (a) $\cos 270^{\circ}=$ $\square$ 0 Undefined (b) $\tan 270^{\circ}$ Undefined (c) $\cos 540^{\circ}=$ $\square$ Undefined (d) $\tan 540^{\circ}=$ $\square$ Undefined (e) $\tan -30^{\circ}=$ $\square$ Undefined

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Problem 845

Find the vertical asymptotes of the function $h(\theta)=\tan \theta+2$ in the interval $0 \leq \theta \leq 2 \pi$ .
Number of asymptotes: Choose one

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Problem 846

$\sin ^{-1}\left(\frac{-\sqrt{3}}{3}\right)$

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Problem 847

Using the Law of Sines to solve the all possible triangles if $\angle A=120^{\circ}, a=30, b=17$ . If no answer exists, enter DNE for all answers. $\angle B$ is $\square$ degrees $\angle C$ is $\square$ degrees $c=$ $\square$ Assume $\angle A$ is opposite side $a, \angle B$ is opposite side $b$ , and $\angle C$ is opposite side $c$ .

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Problem 848

Using the Law of Sines to solve the all possible triangles if $\angle B=50^{\circ}, a=100, b=45$ . Round to 3 decimal places. If no answer exists, enter DNE for all answers. $\begin{aligned} \angle A & =\square \text { degrees } \\ \angle C & =\square \text { degrees } \\ c & =\square \end{aligned}$
Assume $\angle A$ is opposite side $a, \angle B$ is opposite side $b$ , and $\angle C$ is opposite side $c$ .

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Problem 849

Solve each triangle $A B C$ that exists. $A=40.5^{\circ} \quad a=8.8 m \quad b=10.7 m$
Select the correct choice below and, if necessary, fill in the answer boxes within the choice. A. There is only one possible solution for the triangle.
The measurements for the remaining angles B and C and side C are as follows. $\mathrm{B}=\square^{\circ}$ $\mathrm{C}=$ $\square$ $c=$ $\square$ (Round to the nearest (Round to the nearest (Round to the nearest tenth tenth as needed.) tenth as needed.) as needed.) B. There are two possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. $B_{1}=$ $\square$ (Round to the nearest $\mathrm{C}_{1}=$ $\square$ $c_{1}=$ $\square$ tenth as needed.) (Round to the nearest (Round to the nearest tenth The measurements for the tenth as needed.) as needed.) $B_{2}=$ $\square$ $\mathrm{C}_{2}=$ $\square$ (Round to the nearest (Round to the nearest tenth as needed.) tenth as needed.) $c_{2}=\square$ (Round to the nearest tenth as needed.) C. There are no possible solutions for this triangle.

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Problem 850

Find all solutions on the interval $\left[0^{\circ}, 360^{\circ}\right)$ . Use exact values. $18 \cos ^{2} x-9 \cos x-9=0$

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Problem 851

18. Using sketches of $f(x)=\frac{1}{\sec x}$ and $g(x)=\frac{1}{\sin x}$ , determine where $\sec x \geq \csc x$ for $0^{r} \leq x \leq 2 \pi^{r}$ . State your answer using interval notation. Include any asymptotes in your sketches. 5]

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Problem 852

18. Using sketches of $f(x)=\sec x$ and $g(x)=\csc x$ , determine where $\sec x>\csc x$ for $0^{r} \leq x \leq 2 \pi^{r}$ . State your answer using interval notation. Include any asymptotes in your sketches.

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Problem 853

1) Simplify. a) $\sin x\left(\frac{1}{\cos x}\right)$ b) $(\cos x)(\sec x)$ c) $1-\cos ^{2} x$ d) $1-\sin ^{2} x$ e) $\frac{\tan x}{\sin x}$ f) $(1-\sin x)(1+\sin x)$ g) $\left(\frac{1}{\tan x}\right) \sin x$ h) $\frac{1+\tan ^{2} x}{\tan ^{2} x}$ i) $\frac{\sin x \cos x}{1-\sin ^{2} x}$ j) $\frac{1-\cos ^{2} x}{\sin x \cos x}$

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Problem 854

Indicate whether the following statements are true or false.
A periodic graph repeats itself at regular intervals. Choose...
The period of a periodic function is equal to twice the length of one cycle. Choose... Choose...
The period of the graph above is 6 .

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Problem 855

A radio tower is located 275 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $37^{\circ}$ and that the angle of depression to the bottom of the tower is $20^{\circ}$ . How tall is the tower? $\square$ feet
Give your answer rounded to the nearest foot.

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Problem 856

Use the ALEKS calculator to evaluate each expression. Give your answers in radians. Round them to the nearest hundredth. If applicable, click on "Undefined." $\begin{array}{c} \sin ^{-1}(1.33)=\square \\ \tan ^{-1}(3.21)=\square \\ \cos ^{-1}(-0.64)=\square \end{array}$

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Problem 857

12) $\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}=2 \sec ^{2} \theta$

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Problem 858

15) $\frac{\sec \theta+1}{\sec \theta-1}+\frac{\cos \theta+1}{\cos \theta-1}=0$

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Problem 859

Question If the terminal side of angle $\theta$ intersects the unit circle at the point $\left(-\frac{4}{5}, \frac{3}{5}\right)$ , find $\sec (\theta)$ .
Provide your answer below:

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Problem 860

Question Enter the equation of the function $\sin (x)$ that has a vertical shift 4 units down and a phase shift of $\frac{\pi}{3}$ units left.
Provide your answer below:

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Problem 861

Question Determine the magnitude and direction of the vertical shift and the phase shift for the function below. $f(x)=\sin \left(x+\frac{\pi}{4}\right)-2$
Select the correct answer below: The vertical shift is 2 units up, and the phase shift is $\frac{\pi}{4}$ units left. The vertical shift is $\frac{\pi}{4}$ units up, and the phase shift is 2 units right. The vertical shift is $\frac{\pi}{4}$ units down, and the phase shift is 2 units left. The vertical shift is 2 units down, and the phase shift is $\frac{\pi}{4}$ units left. The vertical shift is 2 uxtys up, and the phase shift is $\frac{\pi}{4}$ units right. The vertical shift is 2 units down, and the phase shift is $\frac{\pi}{4}$ units right. FEEDBACK MORE INSTRUCTION SUBMIT Content attribution

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Problem 862

Question
What is the amplitude and period of the function $f(x)=2 \sin \left(\frac{1}{5} x\right)$ ? Please provide your answer in the form of $\pi$ . Provide your answer below:
Amplitude is $\square$ period is $\square$

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Problem 863

9. Two forest fire stations, $P$ and $Q$ , are 20.0 km apart. A ranger at station $Q$ sees a fire 15.0 km away. If the angle between the line $P Q$ and the line from $P$ to the fire is $25^{\circ}$ , how far, to the nearest tenth of a kilometre, is station $P$ from the fire?

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Problem 864

Question Find the equation of the graph given below using the points provided. Notice that the cosine function is used in the answer template, representing a cosine function that is shifted and/or reflected.
Use the variable $x$ in your equation, but be careful not use the multiplication $x^{\prime}$ symbol.
Provide your answer below: $\mathrm{y}=\square \cos (\square)+(\square)$ FEEDBACK MORE INSTRUCTION SUBMIT

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Problem 865

Select the correct answer below: $y=2 \cos \left(\frac{1}{2} x-\frac{\pi}{4}\right)+2$ $y=-2 \cos \left(\frac{1}{2} x-\frac{\pi}{4}\right)-2$ $y=-2 \cos \left(-\frac{1}{4} x+\frac{\pi}{8}\right)-2$ $y=2 \cos \left(\frac{1}{4} x+\frac{\pi}{8}\right)-2$ $y=2 \cos \left(\frac{1}{2} x+\frac{\pi}{4}\right)+2$ $y=-2 \cos \left(\frac{1}{2} x+\frac{\pi}{4}\right)-2$

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Problem 866

Find the smallest positive angle (in degrees) coterminal with $A = 142^{\circ}$ .

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Problem 867

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

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Problem 868

Convert the angle $-81^{\circ} 33^{\prime}$ to decimal degrees.

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Problem 869

Find $\csc \theta$ if $\cot \theta = -\frac{1}{5}$ and $\theta$ is in quadrant IV.

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Problem 870

Find $\cos \theta$ if $\sin \theta=\frac{12}{13}$ and $\theta$ is in quadrant II.

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Problem 871

Find the six trigonometric functions for $\theta$ with point $P(-7,4)$ on its terminal side.

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Problem 872

Find the height of a mountain peak given a distance of 27.2193 miles and an angle of elevation of $5.75^{\circ}$ .

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Problem 873

Find $\sec \theta$ given that $\cos \theta = \frac{7}{8}$ .

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Problem 874

Find $\cot \theta$ using the reciprocal identity if $\tan \theta = 6$ .

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Problem 875

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{117}}{3}$ . Rationalize denominators if needed.

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Problem 876

Find $\sin \theta$ given $\csc \theta = \frac{\sqrt{28}}{4}$ . Rationalize denominators if needed.

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Problem 877

Find $\sin \theta$ if $\csc \theta = 31.25$ .

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Problem 878

Find $\sin \theta$ using the identity, given that $\csc \theta = 6.4$ .

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Problem 879

Determine the quadrants for angle $\theta$ where $\cos \theta > 0$ and $\sin \theta < 0$ .

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Problem 880

Is it possible for $\sin \theta$ to equal 2?

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Problem 881

Determine the quadrants where $\csc \alpha > 0$ and $\cos \alpha > 0$ .

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Problem 882

Is it possible for $\sin 0$ to equal -5?

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Problem 883

Find $\cos \theta$ if $\sin \theta=\frac{4}{5}$ and $\theta$ is in quadrant II. Rationalize if needed.

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Problem 884

Is the equation $\sin \theta = 6$ possible or impossible?

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Problem 885

Find all trigonometric functions of $\theta$ if $\tan \theta=\frac{4}{3}$ and $\theta$ is in quadrant 1.

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Problem 886

Find the other trigonometric functions of $\theta$ if $\sin \theta=\frac{\sqrt{3}}{6}$ and $\cos \theta>0$ .

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Problem 887

Determine if $\csc \left[(4 n+3) \cdot 90^{\circ}\right]$ equals $0, 1, -1$ , or is undefined for integer $n$ .

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Problem 888

Find the sign of $\csc \left(\theta+180^{\circ}\right)$ for $90^{\circ}<\theta<180^{\circ}$ .

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Problem 889

Evaluate the expression using trigonometric values of quadrantal angles: $(\cos 180^{\circ})^{2} - (\sin 360^{\circ})^{2}$

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Problem 890

Evaluate $5 \tan 0^{\circ} + 6 \csc 90^{\circ}$ .

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Problem 891

Find the value of $\csc 4590^{\circ}$ or state if it is undefined.

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Problem 892

Find the six trigonometric functions of angle $\theta$ given the line $3x+y=0$ with $x \leq 0$ .

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Problem 893

Sketch the least positive angle $\theta$ from the line $-7x - 3y = 0$ where $x \leq 0$ , and find the six trig functions of $\theta$ .

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Problem 894

Find the six trigonometric functions for the angle $765^{\circ}$ . Calculate $\sin 765^{\circ}=$ (simplify and rationalize).

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Problem 895

Find the six trigonometric functions for the angle $-510^{\circ}$ . Calculate $\sin \left(-510^{\circ}\right)$ .

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Problem 896

Find the exact value of $\sin 1935^{\circ}$ . Simplify your answer using integers or fractions.

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Problem 897

Complete the table for $\theta = 225^{\circ}$ : find $\cos \theta$ and $\cot \theta$ given $\sin \theta = -\frac{\sqrt{2}}{2}$ .

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Problem 898

Find the exact value of $\sin(-855^\circ)$ . Simplify your answer, using integers or fractions.

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Problem 899

Find the exact value of $\sec(-150^\circ)$ . Simplify your answer using integers or fractions.

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Problem 900

Find all $\theta$ in $[0^{\circ}, 360^{\circ})$ where $\sin \theta=\frac{\sqrt{3}}{2}$ . What is $\theta$ ?

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Trigonometry

Problem 801

Write the expression in terms of first powers of cosine. Do not use decimals in your answer. Make sure to simplify as much as possible. sin⁡4x=\sin ^{4} x=sin4x= □\square□ cos⁡\coscos □\square□

Problem 802

Problem 803

Problem 804

Problem 805

Problem 806

Problem 807

Find the reference angle for 41π12\frac{41 \pi}{12}1241π​.

Problem 808

Let θ\thetaθ be an angle in quadrant IV such that csc⁡θ=−53\csc \theta=-\frac{5}{3}cscθ=−35​. Find the exact values of tan⁡θ\tan \thetatanθ and cos⁡θ\cos \thetacosθ. tan⁡θ=\tan \theta=tanθ= □\square□ cos⁡θ=\cos \theta=cosθ= □\square□

Problem 809

If θ=240∘\theta=240^{\circ}θ=240∘, find the exact value of each expression below. (a) 2cos⁡θ=2 \cos \theta=2cosθ= □\square□ (b) cos⁡θ2=\quad \cos \frac{\theta}{2}=cos2θ​= □\square□ (c) cos⁡2θ=\cos ^{2} \theta=cos2θ= □\square□

Problem 810

Problem 811

Problem 812

40- Two vectors have magnitudes of 10 m and 15 m . The angle between them when they are drawn with their tails at the same point is 65∘65^{\circ}65∘. The component of the longer vector along the line of the shorter is: A. 0 B. 4.2 m C. 6.3 m D. 9.1 m E. 14 m

Problem 813

Problem 814

5sin⁡xcos⁡x+cos⁡x=05 \sin x \cos x+\cos x=05sinxcosx+cosx=0

Problem 815

Solve cos⁡2(x)=−8sin⁡(x)\cos ^{2}(x)=-8 \sin (x)cos2(x)=−8sin(x) for all solutions 0≤x<2π0 \leq x<2 \pi0≤x<2π. x=x=x=

Problem 816

Convert the angle 3π5\frac{3 \pi}{5}53π​ from radians to degrees.

Problem 817

Find the exact value of cos⁡2π9cos⁡π18+sin⁡2π9sin⁡π18\cos \frac{2 \pi}{9} \cos \frac{\pi}{18}+\sin \frac{2 \pi}{9} \sin \frac{\pi}{18}cos92π​cos18π​+sin92π​sin18π​

Problem 818

Sketch an angle θ\thetaθ with the point (−6,0)(-6,0)(−6,0) on its terminal side. Find the six trig functions of θ\thetaθ.

Problem 819

Determine if sin⁡[(4n+3)⋅90∘]\sin \left[(4 n+3) \cdot 90^{\circ}\right]sin[(4n+3)⋅90∘] equals 0, 1, -1, or is undefined for integer nnn.

Problem 820

Determine if the ratio yr\frac{y}{r}ry​ is positive or negative for the point (x,y)(x, y)(x,y) in quadrant II, where r=x2+y2r=\sqrt{x^{2}+y^{2}}r=x2+y2​.

Problem 821

Find the value of cos⁡(0∘)\cos(0^{\circ})cos(0∘).

Problem 822

Find the value of sec⁡180∘\sec 180^{\circ}sec180∘.

Problem 823

Find the value of tan⁡900∘\tan 900^{\circ}tan900∘.

Problem 824

Find the value of cos⁡1800∘\cos 1800^{\circ}cos1800∘.

Problem 825

Find the value of csc⁡3150∘\csc 3150^{\circ}csc3150∘.

Problem 826

Trova il periodo della funzione y=sin⁡23xy=\sin \frac{2}{3} xy=sin32​x.

Problem 827

Determine the period of the function y=2cos⁡2x+sin⁡xy=2 \cos 2x + \sin xy=2cos2x+sinx.

Problem 828

Note: Triangle may not be drawn to scale. Suppose c=9\mathrm{c}=9c=9 and A=35\mathrm{A}=35A=35 degrees. Find: a=a=a= b=b=b= B=B=B= □\square□ degrees

Problem 829

Solve for xxx. Round to the nearest tenth, if necessary.

Problem 830

tan⁡2(θ)−1=0\tan ^{2}(\theta)-1=0tan2(θ)−1=0

Problem 831

2cos⁡2(θ)−cos⁡(θ)−1=02 \cos ^{2}(\theta)-\cos (\theta)-1=02cos2(θ)−cos(θ)−1=0

Problem 832

Problem 833

anie Dads.Question Watch VideoFind an angle θ\thetaθ coterminal to 1163∘1163^{\circ}1163∘, where 0∘≤θ<360∘0^{\circ} \leq \theta<360^{\circ}0∘≤θ<360∘.Answer Attempt 1 out of 2 □\square□ Submit Answer

Problem 834

Problem 835

The Washington Monument is 555 ft tall. The angle of elevation from the end of the monument's shadow to the top of the monument has a cosecant of 1.10. a. θ=\theta=θ= □\square□ (Type your answer in degrees. Rou

Problem 836

Show ExamplesThe terminal ray of an angle θ\thetaθ intersects the unit circle as shown below. Use the given coordinates to calculate cos⁡θ\cos \thetacosθ rounded to three decimal places, if necessary. Answer Attempt 1 put of 2

Problem 837

Problem 838

1+1tan⁡2x=1sin⁡2x1+\frac{1}{\tan ^{2} x}=\frac{1}{\sin ^{2} x}1+tan2x1​=sin2x1​

Problem 839

Problem 840

Problem 841

Problem 842

Problem 843

Problem 844

Problem 845

Find the vertical asymptotes of the function h(θ)=tan⁡θ+2h(\theta)=\tan \theta+2h(θ)=tanθ+2 in the interval 0≤θ≤2π0 \leq \theta \leq 2 \pi0≤θ≤2π.Number of asymptotes: Choose one

Problem 846

sin⁡−1(−33)\sin ^{-1}\left(\frac{-\sqrt{3}}{3}\right)sin−1(3−3​​)

Problem 847

Problem 848

Problem 849

Problem 850

Write the expression in terms of first powers of cosine. Do not use decimals in your answer. Make sure to simplify as much as possible. $\sin ^{4} x=$ $\square$
$\cos$ $\square$

Find the reference angle for $\frac{41 \pi}{12}$ .

Let $\theta$ be an angle in quadrant IV such that $\csc \theta=-\frac{5}{3}$ . Find the exact values of $\tan \theta$ and $\cos \theta$ . $\tan \theta=$ $\square$ $\cos \theta=$ $\square$

If $\theta=240^{\circ}$ , find the exact value of each expression below. (a) $2 \cos \theta=$ $\square$ (b) $\quad \cos \frac{\theta}{2}=$ $\square$ (c) $\cos ^{2} \theta=$ $\square$

40- Two vectors have magnitudes of 10 m and 15 m . The angle between them when they are drawn with their tails at the same point is $65^{\circ}$ . The component of the longer vector along the line of the shorter is: A. 0 B. 4.2 m C. 6.3 m D. 9.1 m E. 14 m

$5 \sin x \cos x+\cos x=0$

Solve $\cos ^{2}(x)=-8 \sin (x)$ for all solutions $0 \leq x<2 \pi$ . $x=$

Convert the angle $\frac{3 \pi}{5}$ from radians to degrees.

Find the exact value of $\cos \frac{2 \pi}{9} \cos \frac{\pi}{18}+\sin \frac{2 \pi}{9} \sin \frac{\pi}{18}$

Sketch an angle $\theta$ with the point $(-6,0)$ on its terminal side. Find the six trig functions of $\theta$ .

Determine if $\sin \left[(4 n+3) \cdot 90^{\circ}\right]$ equals 0, 1, -1, or is undefined for integer $n$ .

Determine if the ratio $\frac{y}{r}$ is positive or negative for the point $(x, y)$ in quadrant II, where $r=\sqrt{x^{2}+y^{2}}$ .

Find the value of $\cos(0^{\circ})$ .

Find the value of $\sec 180^{\circ}$ .

Find the value of $\tan 900^{\circ}$ .

Find the value of $\cos 1800^{\circ}$ .

Find the value of $\csc 3150^{\circ}$ .

Trova il periodo della funzione $y=\sin \frac{2}{3} x$ .

Determine the period of the function $y=2 \cos 2x + \sin x$ .

Note: Triangle may not be drawn to scale. Suppose $\mathrm{c}=9$ and $\mathrm{A}=35$ degrees. Find: $a=$ $b=$ $B=$ $\square$ degrees

Solve for $x$ . Round to the nearest tenth, if necessary.

$\tan ^{2}(\theta)-1=0$

$2 \cos ^{2}(\theta)-\cos (\theta)-1=0$

anie Dads.
Question Watch Video
Find an angle $\theta$ coterminal to $1163^{\circ}$ , where $0^{\circ} \leq \theta<360^{\circ}$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

The Washington Monument is 555 ft tall. The angle of elevation from the end of the monument's shadow to the top of the monument has a cosecant of 1.10. a. $\theta=$ $\square$ (Type your answer in degrees. Rou

Show Examples
The terminal ray of an angle $\theta$ intersects the unit circle as shown below. Use the given coordinates to calculate $\cos \theta$ rounded to three decimal places, if necessary. Answer Attempt 1 put of 2

$1+\frac{1}{\tan ^{2} x}=\frac{1}{\sin ^{2} x}$

Find the vertical asymptotes of the function $h(\theta)=\tan \theta+2$ in the interval $0 \leq \theta \leq 2 \pi$ .
Number of asymptotes: Choose one

$\sin ^{-1}\left(\frac{-\sqrt{3}}{3}\right)$

Find all solutions on the interval $\left[0^{\circ}, 360^{\circ}\right)$ . Use exact values. $18 \cos ^{2} x-9 \cos x-9=0$

18. Using sketches of $f(x)=\sec x$ and $g(x)=\csc x$ , determine where $\sec x>\csc x$ for $0^{r} \leq x \leq 2 \pi^{r}$ . State your answer using interval notation. Include any asymptotes in your sketches.

Indicate whether the following statements are true or false.
A periodic graph repeats itself at regular intervals. Choose...
The period of a periodic function is equal to twice the length of one cycle. Choose... Choose...
The period of the graph above is 6 .

12) $\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}=2 \sec ^{2} \theta$

15) $\frac{\sec \theta+1}{\sec \theta-1}+\frac{\cos \theta+1}{\cos \theta-1}=0$

Question If the terminal side of angle $\theta$ intersects the unit circle at the point $\left(-\frac{4}{5}, \frac{3}{5}\right)$ , find $\sec (\theta)$ .
Provide your answer below:

Question Enter the equation of the function $\sin (x)$ that has a vertical shift 4 units down and a phase shift of $\frac{\pi}{3}$ units left.
Provide your answer below:

Question
What is the amplitude and period of the function $f(x)=2 \sin \left(\frac{1}{5} x\right)$ ? Please provide your answer in the form of $\pi$ . Provide your answer below:
Amplitude is $\square$ period is $\square$

9. Two forest fire stations, $P$ and $Q$ , are 20.0 km apart. A ranger at station $Q$ sees a fire 15.0 km away. If the angle between the line $P Q$ and the line from $P$ to the fire is $25^{\circ}$ , how far, to the nearest tenth of a kilometre, is station $P$ from the fire?

Find the smallest positive angle (in degrees) coterminal with $A = 142^{\circ}$ .

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

Convert the angle $-81^{\circ} 33^{\prime}$ to decimal degrees.

Find $\csc \theta$ if $\cot \theta = -\frac{1}{5}$ and $\theta$ is in quadrant IV.

Find $\cos \theta$ if $\sin \theta=\frac{12}{13}$ and $\theta$ is in quadrant II.

Find the six trigonometric functions for $\theta$ with point $P(-7,4)$ on its terminal side.

Find the height of a mountain peak given a distance of 27.2193 miles and an angle of elevation of $5.75^{\circ}$ .

Find $\sec \theta$ given that $\cos \theta = \frac{7}{8}$ .

Find $\cot \theta$ using the reciprocal identity if $\tan \theta = 6$ .