Identities & Equations

Problem 401

Question 19
Solve for the exact solutions in the interval $[0, 2\pi)$ . List your answers separated by a comma, if it has no real solutions, enter DNE.
$\sin(\frac{x}{2}) = \sqrt{2} - \sin(\frac{x}{2})$
Submit Question

See Solution

Problem 402

Evaluate the expression $\cos^{-1}\left(\sin\left(\frac{4\pi}{3}\right)\right)$ .

See Solution

Problem 403

$\sin \theta = \frac{\sqrt{3}}{3}$ , $\frac{\pi}{2} < \theta < \pi$ (a) $\sin(2\theta) =$ (Type an exact answer, using radicals as needed.) (b) $\cos(2\theta)$ (c) $\sin \frac{\theta}{2}$ (d) $\cos \frac{\theta}{2}$ Use the information given about the angle $\theta$ to find the exact values of the following. Question 28, 7.6.13 Part 1 of 4 LM est. 60 min

See Solution

Problem 404

6 Se $x \in \left[ -\frac{\pi}{2}; 0 \right]$ e $\cos\left(x - \frac{\pi}{4}\right) = \cos\left(2x + \frac{\pi}{3}\right)$ allora $x$ è uguale a: a $-\frac{\pi}{6}$ b $-\frac{\pi}{12}$ c $-\frac{\pi}{18}$ d $-\frac{\pi}{36}$

See Solution

Problem 405

Question 3 (1 point) Factor the expression $\sin ^{2} \theta-\sin \theta-12$ . $(\sin \theta-3)(\sin \theta+4)$ $(\sin \theta-1)(\sin \theta+12)$ $(\sin \theta+3)(\sin \theta-4)$ $(\sin \theta-6)(\sin \theta+2)$

See Solution

Problem 406

How many solutions does the equation $\frac{\cos{x} + 1}{2} = 1$ have for $0 \le x \le 2\pi$ ? 1 2 3 4

See Solution

Problem 407

Use the cosine of a sum and cosine of a difference identities to find $\cos (s + t)$ and $\cos (s - t)$ . $\sin s = -\frac{4}{5}$ and $\sin t = \frac{12}{13}$ , $s$ in quadrant III and $t$ in quadrant I $\cos (s + t) = \square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

See Solution

Problem 408

conseille de refaire les roues de sorte que l'angle $\alpha \in [0; \frac{\pi}{3}]$ entre deux rayons successifs vérifie la relation : $\sqrt{3}\cos{2\alpha} + \sin{2\alpha} = 1$ .
Etant donné que ni Koffi, ni son soudeur n'a de connaissances en Mathématiques, il sollicite son fils Tano, votre camarade de classe pour déterminer le nombre de rayons qu'il faudra avoir sur chaque nouvelle roue. En utilisant votre connaissance mathématique au programme, Aidez votre camarade à trouver une solution au problème de son père.

See Solution

Problem 409

Simplify $\frac{\sin(t)}{\sec(t) - \cos(t)}$ to a single trig function.

See Solution

Problem 410

$\sec (x) \cot (x)=$
A $\sin (x)$
B $\cos (\mathrm{x})$
C $\tan (x)$
D $\sec (x)$ $E \quad \csc (x)$

See Solution

Problem 411

Convert $r=4 \cos (\theta)$ to a rectangular equation.

See Solution

Problem 412

$\begin{array}{l} \frac{\cos 2 x-\cos 4 x}{\sin 2 x+\sin 4 x}= \\ \frac{\cos 2 x+\cos 4 x}{\sin 2 x-\sin 4 x}= \end{array}$ $\tan x$ $\qquad$ cots -Cot $x$ $\sin x$ $-\tan x$

See Solution

Problem 413

3
Select the correct answer.
Convert $x=4$ to polar form. A. $r=4 \sin \theta$ B. $r=\frac{\cos \theta}{4}$ C. $r=\frac{4}{\cos \theta}$ D. $r=4$ E. $r=\frac{4}{\sec \theta}$

See Solution

Problem 414

1. $\cos (\pi / 9) \cong 0.9397$ . use equivalent trigonometric expression to evaluate $\sin (7 \pi / 18)$ Show at least three lines of work for full marks. 2 marks
2. Use trigonometric identities and compound angle formulas to calculate the exact value of $\sin \frac{19 \pi}{22}$ , Simplify your answer and rationalize denominators. Show at least four lines of work for full marks, 4 marks

See Solution

Problem 415

7. Write the expression $\cot ^{2} \theta+\tan ^{2} \theta-\csc ^{2} \theta+2$ as a single term. [sect. 9.4] A. $-\cos ^{2} \theta$ B. $\sec \theta$ C. $-\sec ^{2} \theta$ D. $\sec ^{2} \theta$

See Solution

Problem 416

Prove that $\frac{2 \cos (x)-1}{2 \cos ^{2}(x)-7 \cos (x)+3}=\frac{1}{\cos x-3}$ is an identity.

See Solution

Problem 417

$\begin{array}{l}\frac{1}{2} \cos 540^{\circ}+\frac{2}{3} \sin 720^{\circ}-\frac{1}{4} \sin 450^{\circ}+6 \sin \left(-270^{\circ}\right) \\ \cos 4 \pi+2 \sin \left(-\frac{15}{2} \pi\right)+\frac{1}{3} \cos (-3 \pi)+\sin \frac{9}{2} \pi \\ \frac{\sin \frac{7}{2} \pi-\cos (-7 \pi)+2 \sin \left(-\frac{11}{2} \pi\right)}{2 \sin \left(-\frac{3}{2} \pi\right)+\cos 4 \pi-4 \cos \frac{5}{2} \pi} \\ \frac{4\left(\cos ^{2} 2 \pi+\sin ^{2} \frac{5}{2} \pi\right)+8 \cos 10 \pi}{3[1-4 \cos (-4 \pi)]}\end{array}$

See Solution

Problem 418

285 $\cos \alpha=\frac{2}{3} \mathrm{e} \frac{3}{2} \pi<\alpha<2 \pi ; \sin \alpha$ ? 186 $197 \sin \alpha=-\frac{12}{13} \mathrm{e} b \in$ III quadrante; $\cos \alpha$ ? $138 \sin \alpha=\frac{\sqrt{5}}{3}$ e $b \in$ II quadrante; $\cos \alpha$ ?

See Solution

Problem 419

EUREKAL 544 Scrivi un quadrato di binomio dal quale si ottiene $1-2 \sin \alpha \cos \alpha$ .

See Solution

Problem 420

Find the exact value of $\tan^{-1}\left[\tan\left(\frac{5\pi}{7}\right)\right]$ without a calculator.

See Solution

Problem 421

Find $\sin 2 x, \cos 2 x$ , and $\tan 2 x$ if $\sin x=\frac{1}{\sqrt{10}}$ and $x$ terminates in quadrant II. $\sin 2 x=$ $\square$ $\cos 2 x=$ $\square$

See Solution

Problem 422

Homework
Quizzes \& Tests Study Plan Gradebook eText Chapter Contents > Skills for Success
Tools for Success
Multimedia Library Learning Guide
Purchase Options
Document Sharing Homework: HW 4.1-4.2-4.3 Question 20, 4.3.VQ-3 HW Score: 56\%, 14 of 25 Help Part 1 of 4 points Points: 0 of 1 Save
Question list Question 19 Question 20 Question 21 Question 22 Question 23 Question 24 Question 25
Watch the video and then solve the problem given below. Click here to watch the video. - The angle $t$ is an acute angle and $\boldsymbol{\operatorname { s i n }} t$ and $\boldsymbol{\operatorname { c o s }} t$ are given. Use identities to find $\tan t, \csc t, \sec t$ , and $\cot t$ . Where necessary, rationalize denominators. $\sin t=\frac{1}{6}, \cos t=\frac{\sqrt{35}}{6}$ $\boldsymbol{\operatorname { t a n }} \mathrm{t}=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) Incorrect: 0

See Solution

Problem 423

Find all exact solutions on the interval $[0,2 \pi)$ . If there is more than one answer, enter them as a comma separated list. $\begin{array}{l} 2 \cos ^{2}(t)+\cos (t)=1 \\ t=\square \text { help (angles). } \end{array}$

See Solution

Problem 424

L'equazione $\cos x=\frac{1}{17}$ a ha quattro soluzioni c. ha più di 6 soluzioni b equivale all'equazione sen $x=\frac{12}{17} \sqrt{2}$ d ha un'unica soluzione

See Solution

Problem 425

Which of the following expressions is NOT equivalent to $\sin 75^{\circ}$ ? a. $\sin 45^{\circ}+\sin 30^{\circ}$ b. $\sin \left(45^{\circ}+30^{\circ}\right)$ c. $\sin 45^{\circ} \cos 30^{\circ}+\sin 30^{\circ} \cos 45^{\circ}$ d. $\sin 105^{\circ}$
2. Simplify the expression $\frac{\tan \frac{5 \pi}{8}-\tan \frac{3 \pi}{8}}{1+\tan \frac{5 \pi}{8} \tan \frac{3 \pi}{8}}$ . A. 0 o. undefined b. 1 d. -1
3. Which expression is a proper simplification of $2 \sin \frac{x}{2} \cos \frac{x}{2}$ ?
4. Pactor the expression $81-16 \sin ^{2} \theta$ . a. $(9-4 \sin \theta)^{2}$ c. $\left(3-2 \sin ^{2} \theta\right)^{4}$ я. $\sin \frac{x}{2}$ b. $3\left(27-5 \sin ^{2} \theta\right)$ d. $(9+4 \sin \theta)(9-4 \sin \theta)$ b. $\sin (4 x)$ c. $\sin (2 x)$ d. $\sin x$

See Solution

Problem 426

a) Решите уравнение: $\left(36^{\sin (x)}\right)^{\cos (x)}=6^{\sqrt{2} \sin (x)}$ б) Укажите корни этого уравнения, принадлежащие интервалу: $[8 \pi ; 9 \pi]$

See Solution

Problem 427

10 Se arcsen $x=\frac{2}{5} \pi$ , quanto vale arccos $x$ ? (a) $\frac{\pi}{5}$ [c] $\frac{3}{10} \pi$ [b] $\frac{3}{5} \pi$ []. $\frac{\pi}{10}$

See Solution

Problem 428

Select the correct answer.
In right triangle $A B C, \angle A$ and $\angle \boldsymbol{B}$ are complementary angles and $\sin A=\frac{B}{9}$ . What is $\cos B$ ? A. $\frac{8 \sqrt{17}}{17}$ B. $\frac{8}{9}$ C. $\frac{\sqrt{17}}{9}$ D. $\frac{\sqrt{17}}{8}$

See Solution

Problem 429

Solve the equation: $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2 \operatorname{cosec} A$ .

See Solution

Problem 430

Using Half-Angle Formulas In Exercises $73, \underline{74}, \underline{75}$ , and $\underline{76}$ , use the given conditions to a. determine the quadrant in which $u / 2$ lies, and b. find the exact values of $\sin (u / 2), \cos (u / 2)$ , and $\tan (u / 2)$ using the half-angle formulas.
73. $\tan u=\frac{4}{3}, \quad \pi<u<\frac{3 \pi}{2}$
Answer

See Solution

Problem 431

30. Find the exact values. a) $\cos 15^{\circ}$ b) $\sin \frac{11 \pi}{12}$

See Solution

Problem 432

Given that $\sin \theta=-\frac{1}{3}$ and that $\cos \theta<0$ , then determine the exact value of $\tan \theta$ Select one: a. $-\sqrt{8}$ b. $\frac{1}{\sqrt{8}}$ c. $\sqrt{8}$ d. $-\frac{1}{\sqrt{8}}$

See Solution

Problem 433

12. Risolvi l'equazione $2 \cos ^{2}(x)-3 \sin (x)-1=0$ nell'intervallo $[0,2 \pi]$ . (a) $x=\frac{\pi}{4}, \frac{5 \pi}{4}$ (b) $x=\frac{\pi}{6}, \frac{5 \pi}{6}$ (c) $x=\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{4 \pi}{3}, \frac{5 \pi}{3}$ (d) Nessuna soluzione (e) $x=\arcsin \left(-\frac{1}{3}\right), \pi-\arcsin \left(-\frac{1}{3}\right)$

See Solution

Problem 434

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

See Solution

Problem 435

b) $\sin 2 x=2 \sin x \cos x$ c) $\tan x=\frac{\sin x}{\cos x}$ d) all of these - The height of the tip of one blade of a wind turbine above the ground, $h(t)$ , can be modelled by $h(t)=18 \cos \left(\pi t+\frac{\pi}{4}\right)+2$ where $t$ is the time passed in seconds. Whic, time interval describes a period when the bl tip is at least 30 m above the ground? a) $5.24 \leq t \leq 7.33$ (c) $1.37 \leq t \leq 2$ . ) $0.42 \leq t \leq 1.08$ d) $0.08 \leq t \leq 1$ .
Iify $\cos \frac{\pi}{5} \cos \frac{\pi}{6}-\sin \frac{\pi}{5} \sin \frac{\pi}{6}$

See Solution

Problem 436

1. Which of these is an equivalent trigonomerric ratio for $\sin \frac{2 \pi}{5}$ ? a) $\cos \frac{\pi}{10}$ c) $-\cos \frac{9 \pi}{10}$ b) $\sin \frac{3 \pi}{5}$ d) all of these $\alpha=\frac{12}{2}$ and

See Solution

Problem 437

$\cos x \sin x=0$

See Solution

Problem 438

2. If $\sin (\alpha)=\frac{2}{5}$ and $\tan (\beta)=\sqrt{2}$ , where $\frac{\pi}{2} \operatorname{sinsm}$ and $\frac{\pi}{2} s \beta s^{\frac{3 \pi}{2}}$ , calculate $\sin (\alpha+\beta)+\sin (\alpha-\beta)$ . Show at least four lines of work for fult marks. (4 Marks])
3. Determine the exact value of $\operatorname{Cos}(2 x), \operatorname{CSc}(x)=\frac{-17}{15}$ and $\frac{3 \pi}{2} 5 \times \leq 2 \pi$ . Show at least three lines of work for full merts. (4 Marks)

See Solution

Problem 439

$\sin 2x + \sin 2y = 2 \sin (x+y) \cos (x-y)$ Prove this using only the double angle formula, without using the sum-to-product identities.

See Solution

Problem 440

f) $\cos ^{4} \theta-\sin ^{4} \theta=1-2 \sin ^{2} \theta$

See Solution

Problem 441

SITUATION COMPLEXE Koffi est un grand cultivateur de la ville d'Abengourou. Il utilise une charrette pour ramener ses récoltes à la maison. La charrette comporte deux roues dotées chacune de rayons fait en barres de fer par un soudeur comme l'indique la figure ci -- contre. Il voudrait que cette charrette puisse supporter des charges beaucoup plus importantes. Sur ce, son ami Kouman, professeur de MATHS au lycée Moderne d'Abengourou lui
conseille de refaire les roues de sorte que l'angle $\alpha \in$ ]0; $\frac{\pi}{3}$ [ entre deux rayons successifs vérifie la relation : $\sqrt{3}\cos{2\alpha} + \sin{2\alpha} = 1$ .
Etant donné que ni Koffi, ni son soudeur n'a de connaissances en Mathématiques, il sollicite son fils Tano, votre camarade de classe pour déterminer le nombre de rayons qu'il faudra avoir sur chaque nouvelle roue. En utilisant votre connaissance mathématique au programme, Aidez votre camarade à trouver une solution au problème de son père.

See Solution

Problem 442

Which of the following is equivalent to $\frac{\cos (2 \theta)}{\sin ^{2} \theta}$ for all values of $\theta$ for which $\frac{\cos (2 \theta)}{\sin ^{2} \theta}$ is defined?
Select the correct answer below: $\sec \theta-2 \sin \theta \tan \theta$ $2 \cot ^{2} \theta-\csc ^{2} \theta$ $\cot ^{2} \theta-2 \cos ^{2} \theta$ $2 \sin \theta$ $\sin \theta \cos \theta-\tan \theta$

See Solution

Problem 443

2)
If $\sin x=\frac{4}{5}$ and $\sin y=-\frac{12}{13}, 0<x<\frac{\pi}{2}, \frac{3 \pi}{2}<y<2 \pi$ , evaluate can $(x+y)$ [4 marks]

See Solution

Problem 444

2. Determine all values of $x$ on the interval $0^{\circ} \leq x \leq 360^{\circ}$ that satisfy $\cos (2 x)=0$ .

See Solution

Problem 445

6. Solve the equation $5 \cos (2 \alpha)+3=0$ for all values of $\alpha$ on the interval $0^{\circ} \leq \alpha \leq 360^{\circ}$ . Round all answers to the nearest tenth of a degree.

See Solution

Problem 446

3. Provet $\frac{\sin 4 \pm-\sin 2 \pi}{\sin 2 x}=\frac{\cos 3 x}{\cos x}$

See Solution

Problem 447

Evaluate $\sin^{2}(28^{\circ}) + \cos^{2}(28^{\circ})$ and simplify your answer to find the value.

See Solution

Problem 448

Find the exact value of $\cos \frac{\pi}{8}$ .

See Solution

Problem 449

15
Type the correct answer in the box. If necessary, use / for the fraction bar and reduce the fraction.
Complete the statement.
If $\cos \theta=\frac{3}{5}$ and $\theta$ is in quadrant IV, $\sin 2 \theta=$ $\square$

See Solution

Problem 450

Verify that the equation is an identity. $\frac{\csc \alpha}{\cot \alpha}=\sec \alpha$
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. $\frac{\csc \alpha}{\cot \alpha}=\frac{\square}{\square}$
What transforniation is made in the numerator? $\square$ What transformation is made in the denominator? $\square$

See Solution

Problem 451

Find all solutions over the interval $[0,2 \pi]$ given the equation $2 \cos ^{2} \theta+3 \cos \theta=-1$

See Solution

Problem 452

Accelerated Pre-Calculus Seat \# $\qquad$ Date $\qquad$ 4.11a - Homework Educatior Binder S
Part I: New Material - Solving Quadratic Trigonometric Equations A. Directions: Find all solutions to each equation over the interval $[0,2 \pi]$ . Show all wor your final answer.
1. $2 \cos (x)=1$
2. ) $2 \sin ^{2} x+3 \sin x+1=0$

See Solution

Problem 453

B) If $z=\cos 2 \theta+i \sin 2 \theta$ prove that $\frac{Z+1}{Z-1}=-i \cot \theta$

See Solution

1 2 3 4 5

Identities & Equations

Problem 401

Question 19Solve for the exact solutions in the interval [0,2π)[0, 2\pi)[0,2π). List your answers separated by a comma, if it has no real solutions, enter DNE.sin⁡(x2)=2−sin⁡(x2)\sin(\frac{x}{2}) = \sqrt{2} - \sin(\frac{x}{2})sin(2x​)=2​−sin(2x​)Submit Question

Problem 402

Evaluate the expression cos⁡−1(sin⁡(4π3))\cos^{-1}\left(\sin\left(\frac{4\pi}{3}\right)\right)cos−1(sin(34π​)).

Problem 403

Problem 404

Problem 405

Problem 406

How many solutions does the equation cos⁡x+12=1\frac{\cos{x} + 1}{2} = 12cosx+1​=1 have for 0≤x≤2π0 \le x \le 2\pi0≤x≤2π? 1 2 3 4

Problem 407

Problem 408

Problem 409

Simplify sin⁡(t)sec⁡(t)−cos⁡(t)\frac{\sin(t)}{\sec(t) - \cos(t)}sec(t)−cos(t)sin(t)​ to a single trig function.

Problem 410

sec⁡(x)cot⁡(x)=\sec (x) \cot (x)=sec(x)cot(x)=A sin⁡(x)\sin (x)sin(x)B cos⁡(x)\cos (\mathrm{x})cos(x)C tan⁡(x)\tan (x)tan(x)D sec⁡(x)\sec (x)sec(x) Ecsc⁡(x)E \quad \csc (x)Ecsc(x)

Problem 411

Convert r=4cos⁡(θ)r=4 \cos (\theta)r=4cos(θ) to a rectangular equation.

Problem 412

Problem 413

3Select the correct answer.Convert x=4x=4x=4 to polar form. A. r=4sin⁡θr=4 \sin \thetar=4sinθ B. r=cos⁡θ4r=\frac{\cos \theta}{4}r=4cosθ​ C. r=4cos⁡θr=\frac{4}{\cos \theta}r=cosθ4​ D. r=4r=4r=4 E. r=4sec⁡θr=\frac{4}{\sec \theta}r=secθ4​

Problem 414

Problem 415

Problem 416

Prove that 2cos⁡(x)−12cos⁡2(x)−7cos⁡(x)+3=1cos⁡x−3\frac{2 \cos (x)-1}{2 \cos ^{2}(x)-7 \cos (x)+3}=\frac{1}{\cos x-3}2cos2(x)−7cos(x)+32cos(x)−1​=cosx−31​ is an identity.

Problem 417

Problem 418

Problem 419

EUREKAL 544 Scrivi un quadrato di binomio dal quale si ottiene 1−2sin⁡αcos⁡α1-2 \sin \alpha \cos \alpha1−2sinαcosα.

Problem 420

Find the exact value of tan⁡−1[tan⁡(5π7)]\tan^{-1}\left[\tan\left(\frac{5\pi}{7}\right)\right]tan−1[tan(75π​)] without a calculator.

Problem 421

Find sin⁡2x,cos⁡2x\sin 2 x, \cos 2 xsin2x,cos2x, and tan⁡2x\tan 2 xtan2x if sin⁡x=110\sin x=\frac{1}{\sqrt{10}}sinx=10​1​ and xxx terminates in quadrant II. sin⁡2x=\sin 2 x=sin2x= □\square□ cos⁡2x=\cos 2 x=cos2x= □\square□

Problem 422

Problem 423

Problem 424

L'equazione cos⁡x=117\cos x=\frac{1}{17}cosx=171​ a ha quattro soluzioni c. ha più di 6 soluzioni b equivale all'equazione sen x=12172x=\frac{12}{17} \sqrt{2}x=1712​2​ d ha un'unica soluzione

Problem 425

Problem 426

a) Решите уравнение: (36sin⁡(x))cos⁡(x)=62sin⁡(x)\left(36^{\sin (x)}\right)^{\cos (x)}=6^{\sqrt{2} \sin (x)}(36sin(x))cos(x)=62​sin(x) б) Укажите корни этого уравнения, принадлежащие интервалу: [8π;9π][8 \pi ; 9 \pi][8π;9π]

Problem 427

10 Se arcsen x=25πx=\frac{2}{5} \pix=52​π, quanto vale arccos xxx ? (a) π5\frac{\pi}{5}5π​ [c] 310π\frac{3}{10} \pi103​π [b] 35π\frac{3}{5} \pi53​π []. π10\frac{\pi}{10}10π​

Problem 428

Problem 429

Solve the equation: sin⁡A1+cos⁡A+1+cos⁡Asin⁡A=2cosec⁡A\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2 \operatorname{cosec} A1+cosAsinA​+sinA1+cosA​=2cosecA.

Problem 430

Problem 431

30. Find the exact values. a) cos⁡15∘\cos 15^{\circ}cos15∘ b) sin⁡11π12\sin \frac{11 \pi}{12}sin1211π​

Problem 432

Given that sin⁡θ=−13\sin \theta=-\frac{1}{3}sinθ=−31​ and that cos⁡θ<0\cos \theta<0cosθ<0, then determine the exact value of tan⁡θ\tan \thetatanθ Select one: a. −8-\sqrt{8}−8​ b. 18\frac{1}{\sqrt{8}}8​1​ c. 8\sqrt{8}8​ d. −18-\frac{1}{\sqrt{8}}−8​1​

Problem 433

Problem 434

1−2sin⁡2xsin⁡x+cos⁡x+2sin⁡x2cos⁡x2=cos⁡x\frac{1-2 \sin ^{2} x}{\sin x+\cos x}+2 \sin \frac{x}{2} \cos \frac{x}{2}=\cos xsinx+cosx1−2sin2x​+2sin2x​cos2x​=cosx

Problem 435

Problem 436

1. Which of these is an equivalent trigonomerric ratio for sin⁡2π5\sin \frac{2 \pi}{5}sin52π​ ? a) cos⁡π10\cos \frac{\pi}{10}cos10π​ c) −cos⁡9π10-\cos \frac{9 \pi}{10}−cos109π​ b) sin⁡3π5\sin \frac{3 \pi}{5}sin53π​ d) all of these α=122\alpha=\frac{12}{2}α=212​ and

Problem 437

cos⁡xsin⁡x=0\cos x \sin x=0cosxsinx=0

Problem 438

Problem 439

sin⁡2x+sin⁡2y=2sin⁡(x+y)cos⁡(x−y)\sin 2x + \sin 2y = 2 \sin (x+y) \cos (x-y)sin2x+sin2y=2sin(x+y)cos(x−y) Prove this using only the double angle formula, without using the sum-to-product identities.

Problem 440

f) cos⁡4θ−sin⁡4θ=1−2sin⁡2θ\cos ^{4} \theta-\sin ^{4} \theta=1-2 \sin ^{2} \thetacos4θ−sin4θ=1−2sin2θ

Problem 441

Problem 442

Problem 443

2)If sin⁡x=45\sin x=\frac{4}{5}sinx=54​ and sin⁡y=−1213,0<x<π2,3π2<y<2π\sin y=-\frac{12}{13}, 0<x<\frac{\pi}{2}, \frac{3 \pi}{2}<y<2 \pisiny=−1312​,0<x<2π​,23π​<y<2π, evaluate can (x+y)(x+y)(x+y) [4 marks]

Problem 444

2. Determine all values of xxx on the interval 0∘≤x≤360∘0^{\circ} \leq x \leq 360^{\circ}0∘≤x≤360∘ that satisfy cos⁡(2x)=0\cos (2 x)=0cos(2x)=0.

Problem 445

6. Solve the equation 5cos⁡(2α)+3=05 \cos (2 \alpha)+3=05cos(2α)+3=0 for all values of α\alphaα on the interval 0∘≤α≤360∘0^{\circ} \leq \alpha \leq 360^{\circ}0∘≤α≤360∘. Round all answers to the nearest tenth of a degree.

Problem 446

3. Provet sin⁡4±−sin⁡2πsin⁡2x=cos⁡3xcos⁡x\frac{\sin 4 \pm-\sin 2 \pi}{\sin 2 x}=\frac{\cos 3 x}{\cos x}sin2xsin4±−sin2π​=cosxcos3x​

Problem 447

Evaluate sin⁡2(28∘)+cos⁡2(28∘)\sin^{2}(28^{\circ}) + \cos^{2}(28^{\circ})sin2(28∘)+cos2(28∘) and simplify your answer to find the value.

Problem 448

Find the exact value of cos⁡π8\cos \frac{\pi}{8}cos8π​.

Problem 449

15Type the correct answer in the box. If necessary, use / for the fraction bar and reduce the fraction.Complete the statement.If cos⁡θ=35\cos \theta=\frac{3}{5}cosθ=53​ and θ\thetaθ is in quadrant IV, sin⁡2θ=\sin 2 \theta=sin2θ= □\square□

Problem 450

Question 19
Solve for the exact solutions in the interval $[0, 2\pi)$ . List your answers separated by a comma, if it has no real solutions, enter DNE.
$\sin(\frac{x}{2}) = \sqrt{2} - \sin(\frac{x}{2})$
Submit Question

Evaluate the expression $\cos^{-1}\left(\sin\left(\frac{4\pi}{3}\right)\right)$ .

How many solutions does the equation $\frac{\cos{x} + 1}{2} = 1$ have for $0 \le x \le 2\pi$ ? 1 2 3 4

Simplify $\frac{\sin(t)}{\sec(t) - \cos(t)}$ to a single trig function.

$\sec (x) \cot (x)=$
A $\sin (x)$
B $\cos (\mathrm{x})$
C $\tan (x)$
D $\sec (x)$ $E \quad \csc (x)$

Convert $r=4 \cos (\theta)$ to a rectangular equation.

3
Select the correct answer.
Convert $x=4$ to polar form. A. $r=4 \sin \theta$ B. $r=\frac{\cos \theta}{4}$ C. $r=\frac{4}{\cos \theta}$ D. $r=4$ E. $r=\frac{4}{\sec \theta}$

Prove that $\frac{2 \cos (x)-1}{2 \cos ^{2}(x)-7 \cos (x)+3}=\frac{1}{\cos x-3}$ is an identity.

EUREKAL 544 Scrivi un quadrato di binomio dal quale si ottiene $1-2 \sin \alpha \cos \alpha$ .

Find the exact value of $\tan^{-1}\left[\tan\left(\frac{5\pi}{7}\right)\right]$ without a calculator.

Find $\sin 2 x, \cos 2 x$ , and $\tan 2 x$ if $\sin x=\frac{1}{\sqrt{10}}$ and $x$ terminates in quadrant II. $\sin 2 x=$ $\square$ $\cos 2 x=$ $\square$

L'equazione $\cos x=\frac{1}{17}$ a ha quattro soluzioni c. ha più di 6 soluzioni b equivale all'equazione sen $x=\frac{12}{17} \sqrt{2}$ d ha un'unica soluzione

a) Решите уравнение: $\left(36^{\sin (x)}\right)^{\cos (x)}=6^{\sqrt{2} \sin (x)}$ б) Укажите корни этого уравнения, принадлежащие интервалу: $[8 \pi ; 9 \pi]$

10 Se arcsen $x=\frac{2}{5} \pi$ , quanto vale arccos $x$ ? (a) $\frac{\pi}{5}$ [c] $\frac{3}{10} \pi$ [b] $\frac{3}{5} \pi$ []. $\frac{\pi}{10}$

Solve the equation: $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2 \operatorname{cosec} A$ .

30. Find the exact values. a) $\cos 15^{\circ}$ b) $\sin \frac{11 \pi}{12}$

Given that $\sin \theta=-\frac{1}{3}$ and that $\cos \theta<0$ , then determine the exact value of $\tan \theta$ Select one: a. $-\sqrt{8}$ b. $\frac{1}{\sqrt{8}}$ c. $\sqrt{8}$ d. $-\frac{1}{\sqrt{8}}$

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

1. Which of these is an equivalent trigonomerric ratio for $\sin \frac{2 \pi}{5}$ ? a) $\cos \frac{\pi}{10}$ c) $-\cos \frac{9 \pi}{10}$ b) $\sin \frac{3 \pi}{5}$ d) all of these $\alpha=\frac{12}{2}$ and

$\cos x \sin x=0$

$\sin 2x + \sin 2y = 2 \sin (x+y) \cos (x-y)$ Prove this using only the double angle formula, without using the sum-to-product identities.

f) $\cos ^{4} \theta-\sin ^{4} \theta=1-2 \sin ^{2} \theta$

2)
If $\sin x=\frac{4}{5}$ and $\sin y=-\frac{12}{13}, 0<x<\frac{\pi}{2}, \frac{3 \pi}{2}<y<2 \pi$ , evaluate can $(x+y)$ [4 marks]

2. Determine all values of $x$ on the interval $0^{\circ} \leq x \leq 360^{\circ}$ that satisfy $\cos (2 x)=0$ .

6. Solve the equation $5 \cos (2 \alpha)+3=0$ for all values of $\alpha$ on the interval $0^{\circ} \leq \alpha \leq 360^{\circ}$ . Round all answers to the nearest tenth of a degree.

3. Provet $\frac{\sin 4 \pm-\sin 2 \pi}{\sin 2 x}=\frac{\cos 3 x}{\cos x}$

Evaluate $\sin^{2}(28^{\circ}) + \cos^{2}(28^{\circ})$ and simplify your answer to find the value.

Find the exact value of $\cos \frac{\pi}{8}$ .

15
Type the correct answer in the box. If necessary, use / for the fraction bar and reduce the fraction.
Complete the statement.
If $\cos \theta=\frac{3}{5}$ and $\theta$ is in quadrant IV, $\sin 2 \theta=$ $\square$

Find all solutions over the interval $[0,2 \pi]$ given the equation $2 \cos ^{2} \theta+3 \cos \theta=-1$

B) If $z=\cos 2 \theta+i \sin 2 \theta$ prove that $\frac{Z+1}{Z-1}=-i \cot \theta$