Trigonometry

Problem 2201

Calculate the decimal approximation of $\sin 49^{\circ} 24^{\prime}$ , rounding to eight decimal places.

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Problem 2202

Calculate the decimal approximation of $\sin 28^{\circ} 18^{\prime}$ . Round to eight decimal places.

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Problem 2203

A car on a $1.7^{\circ}$ incline has a grade resistance of $123 \, \mathrm{lb}$ . Find the car's weight in hundreds using: Grade Resistance = Weight * sin(incline). Consider other forces too.

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Problem 2204

Find the grade resistance for a 2100-pound car on a $0.5^{\circ}$ uphill grade using $F=W \sin \theta$ . Round to the nearest pound.

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Problem 2205

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

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Problem 2206

Evaluate: $\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}$ . Round to four decimal places.

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Problem 2207

Evaluate $\sin 306^{\circ} \cos 36^{\circ} - \cos 306^{\circ} \sin 36^{\circ}$ using a calculator. Provide a simplified answer.

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Problem 2208

Simplify $\sin 306^{\circ} \cos 36^{\circ}-\cos 306^{\circ} \sin 36^{\circ}=$ (integer or fraction).

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Problem 2209

Find $\alpha$ in $[0^{\circ}, 90^{\circ}]$ such that $\sec \alpha = 1.1556371$ .

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Problem 2210

Find the decimal approximation of $\cot \left(-260^{\circ} 23^{\prime}\right)$ rounded to seven decimal places.

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Problem 2211

Find $\theta$ in $[0^{\circ}, 90^{\circ}]$ such that $\sin \theta = 0.65303571$ . What is $\theta \approx$ ? Round to six decimal places.

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Problem 2212

Find the angle of elevation of the sun for a 64.38 ft tall building with a 69.19 ft shadow. Round to the nearest hundredth.

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Problem 2213

Find the bearing of an airplane at $(12,0)$ from the origin. Provide the bearing as a single angle measure.

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Problem 2214

Find the bearing of an airplane at $(17,0)$ from the origin. Provide both angle measures for the bearing.

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Problem 2215

2) A 0.3 kg ball is tied to a 1 m piece of string and spun so that it is moving in a horizontal circle as shown below. The angle measured between the vertical dashed line and the string is $20^{\circ}$ . Determine angular speed of the ball and tension in the string. $\left[\omega=3.2 \mathrm{rad} \mathrm{~s}^{-1} \text { and } T=3.1 \mathrm{~N}\right]$

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Problem 2216

For the rotation $-\frac{71 \pi}{8}$ , find the coterminal angle from $0 \leq \theta<2 \pi$ , the quadrant, and the reference angle.

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Problem 2217

Find the value of $y$ . Round your answer to the nearest tenth.

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Problem 2218

Find the missing side length. Round to the nearest tenth.

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Problem 2219

$\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}$

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Problem 2220

A bug has fallen into a whirlpool, and it's distance from the center is given by: $r=\theta$ , where $0 \leq \theta \leq 4 \pi$ It is being sucked from the outside towards the center of the swirl in the whirlpool.
What is the horizontal component of the bug's location, after it has spun through an angle of $\frac{11 \pi}{6}$ radians? $x=-4.68$ $x=5.89$ $x=4.99$ $x=9.56$

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Problem 2221

Find an equation for a sinusoidal function that has period $2 \pi$ , amplitude 2 , and contains the point ( $2 \pi, 0$ ).
Write your answer in the form $\mathrm{f}(\mathrm{x})=\mathrm{A} \sin (\mathrm{Bx}+\mathrm{C})+\mathrm{D}$ , where $\mathrm{A}, \mathrm{B}, \mathrm{C}$ , and D are real numbers. $f(x)=$ $\square$

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Problem 2222

Find $x$ . $2 \sqrt{3}$ $8 \sqrt{3}$ 8

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Problem 2223

slove for aictace ond ongle os elvatian

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Problem 2224

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

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Problem 2225

6
A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feer on the wall. Frod to the nearest degree, the angle the ladder makes with the wall. Round to the nearest whole number. Show all work for full credit. $\square$

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Problem 2226

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, $\sin 2 \theta=$ $\square$

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Problem 2227

Find the height of a stone face on a mountain, given angles of elevation of $28^{\circ}$ and $31^{\circ}$ from 800 feet away.

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Problem 2228

Find the value of $\csc (-1305)$ .

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Problem 2229

Find the second least positive value (in radians) for $\beta$ given $11\pi/6$ and for $\gamma$ given $\tan(\gamma)=1$ .

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Problem 2230

If $\tan (\gamma)=1$ , what are the least and second least positive values of $\gamma$ in radians?

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Problem 2231

Prove the trigonometric equation: $\theta \sin \left(\frac{1}{n}\right) \frac{x}{\sqrt{1-x^{2}}} = \tan^{-1}(x)$ .

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Problem 2232

1. In Exercises 53-60, use transformations to describe how the graph of the function is related to a basic trigonometric graph. Graph two periods.
53. $y=\sin (x+\pi)$
54. $y=3+2 \cos x$
55. $y=-\cos (x+\pi / 2)+4$
56. $y=-2-3 \sin (x-\pi)$
57. $y=\tan 2 x$
58. $y=-2 \cot 3 x$
59. $y=-2 \sec \frac{x}{2}$
60. $y=\csc \pi x$

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Problem 2233

Fing the angle of $D$

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Problem 2234

A calculator is allowed for this question. Solve for $x$ (round to the nearest thousandth)

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Problem 2235

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? $\square$

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Problem 2236

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

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Problem 2237

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. ) $2 \sin ^{2} x+3 \sin x+1=0$

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Problem 2238

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

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Trigonometry

Problem 2201

Calculate the decimal approximation of sin⁡49∘24′\sin 49^{\circ} 24^{\prime}sin49∘24′, rounding to eight decimal places.

Problem 2202

Calculate the decimal approximation of sin⁡28∘18′\sin 28^{\circ} 18^{\prime}sin28∘18′. Round to eight decimal places.

Problem 2203

A car on a 1.7∘1.7^{\circ}1.7∘ incline has a grade resistance of 123 lb123 \, \mathrm{lb}123lb. Find the car's weight in hundreds using: Grade Resistance = Weight * sin(incline). Consider other forces too.

Problem 2204

Find the grade resistance for a 2100-pound car on a 0.5∘0.5^{\circ}0.5∘ uphill grade using F=Wsin⁡θF=W \sin \thetaF=Wsinθ. Round to the nearest pound.

Problem 2205

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 2206

Evaluate: sin⁡164∘48′cos⁡15∘12′+cos⁡164∘48′sin⁡15∘12′\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}sin164∘48′cos15∘12′+cos164∘48′sin15∘12′. Round to four decimal places.

Problem 2207

Evaluate sin⁡306∘cos⁡36∘−cos⁡306∘sin⁡36∘\sin 306^{\circ} \cos 36^{\circ} - \cos 306^{\circ} \sin 36^{\circ}sin306∘cos36∘−cos306∘sin36∘ using a calculator. Provide a simplified answer.

Problem 2208

Simplify sin⁡306∘cos⁡36∘−cos⁡306∘sin⁡36∘=\sin 306^{\circ} \cos 36^{\circ}-\cos 306^{\circ} \sin 36^{\circ}=sin306∘cos36∘−cos306∘sin36∘= (integer or fraction).

Problem 2209

Find α\alphaα in [0∘,90∘][0^{\circ}, 90^{\circ}][0∘,90∘] such that sec⁡α=1.1556371\sec \alpha = 1.1556371secα=1.1556371.

Problem 2210

Find the decimal approximation of cot⁡(−260∘23′)\cot \left(-260^{\circ} 23^{\prime}\right)cot(−260∘23′) rounded to seven decimal places.

Problem 2211

Find θ\thetaθ in [0∘,90∘][0^{\circ}, 90^{\circ}][0∘,90∘] such that sin⁡θ=0.65303571\sin \theta = 0.65303571sinθ=0.65303571. What is θ≈\theta \approxθ≈? Round to six decimal places.

Problem 2212

Find the angle of elevation of the sun for a 64.38 ft tall building with a 69.19 ft shadow. Round to the nearest hundredth.

Problem 2213

Find the bearing of an airplane at (12,0)(12,0)(12,0) from the origin. Provide the bearing as a single angle measure.

Problem 2214

Find the bearing of an airplane at (17,0)(17,0)(17,0) from the origin. Provide both angle measures for the bearing.

Problem 2215

Problem 2216

For the rotation −71π8-\frac{71 \pi}{8}−871π​, find the coterminal angle from 0≤θ<2π0 \leq \theta<2 \pi0≤θ<2π, the quadrant, and the reference angle.

Problem 2217

Find the value of yyy. Round your answer to the nearest tenth.

Problem 2218

Find the missing side length. Round to the nearest tenth.

Problem 2219

c=17B=29∘\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}c=17B=29∘​

Problem 2220

Problem 2221

Problem 2222

Find xxx. 232 \sqrt{3}23​ 838 \sqrt{3}83​ 8

Problem 2223

slove for aictace ond ongle os elvatian

Problem 2224

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

Problem 2225

6A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feer on the wall. Frod to the nearest degree, the angle the ladder makes with the wall. Round to the nearest whole number. Show all work for full credit. □\square□

Problem 2226

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 2227

Find the height of a stone face on a mountain, given angles of elevation of 28∘28^{\circ}28∘ and 31∘31^{\circ}31∘ from 800 feet away.

Problem 2228

Find the value of csc⁡(−1305)\csc (-1305)csc(−1305).

Problem 2229

Find the second least positive value (in radians) for β\betaβ given 11π/611\pi/611π/6 and for γ\gammaγ given tan⁡(γ)=1\tan(\gamma)=1tan(γ)=1.

Problem 2230

If tan⁡(γ)=1\tan (\gamma)=1tan(γ)=1, what are the least and second least positive values of γ\gammaγ in radians?

Problem 2231

Prove the trigonometric equation: θsin⁡(1n)x1−x2=tan⁡−1(x)\theta \sin \left(\frac{1}{n}\right) \frac{x}{\sqrt{1-x^{2}}} = \tan^{-1}(x)θsin(n1​)1−x2​x​=tan−1(x).

Problem 2232

Problem 2233

Fing the angle of DDD

Problem 2234

A calculator is allowed for this question. Solve for xxx (round to the nearest thousandth)

Problem 2235

Problem 2236

Find all solutions over the interval [0,2π][0,2 \pi][0,2π] given the equation 2cos⁡2θ+3cos⁡θ=−12 \cos ^{2} \theta+3 \cos \theta=-12cos2θ+3cosθ=−1

Problem 2237

Problem 2238

B) If z=cos⁡2θ+isin⁡2θz=\cos 2 \theta+i \sin 2 \thetaz=cos2θ+isin2θ prove that Z+1Z−1=−icot⁡θ\frac{Z+1}{Z-1}=-i \cot \thetaZ−1Z+1​=−icotθ

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Calculate the decimal approximation of $\sin 49^{\circ} 24^{\prime}$ , rounding to eight decimal places.

Calculate the decimal approximation of $\sin 28^{\circ} 18^{\prime}$ . Round to eight decimal places.

A car on a $1.7^{\circ}$ incline has a grade resistance of $123 \, \mathrm{lb}$ . Find the car's weight in hundreds using: Grade Resistance = Weight * sin(incline). Consider other forces too.

Find the grade resistance for a 2100-pound car on a $0.5^{\circ}$ uphill grade using $F=W \sin \theta$ . Round to the nearest pound.

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

Evaluate: $\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}$ . Round to four decimal places.

Evaluate $\sin 306^{\circ} \cos 36^{\circ} - \cos 306^{\circ} \sin 36^{\circ}$ using a calculator. Provide a simplified answer.

Simplify $\sin 306^{\circ} \cos 36^{\circ}-\cos 306^{\circ} \sin 36^{\circ}=$ (integer or fraction).

Find $\alpha$ in $[0^{\circ}, 90^{\circ}]$ such that $\sec \alpha = 1.1556371$ .

Find the decimal approximation of $\cot \left(-260^{\circ} 23^{\prime}\right)$ rounded to seven decimal places.

Find $\theta$ in $[0^{\circ}, 90^{\circ}]$ such that $\sin \theta = 0.65303571$ . What is $\theta \approx$ ? Round to six decimal places.

Find the bearing of an airplane at $(12,0)$ from the origin. Provide the bearing as a single angle measure.

Find the bearing of an airplane at $(17,0)$ from the origin. Provide both angle measures for the bearing.

For the rotation $-\frac{71 \pi}{8}$ , find the coterminal angle from $0 \leq \theta<2 \pi$ , the quadrant, and the reference angle.

Find the value of $y$ . Round your answer to the nearest tenth.

$\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}$

Find $x$ . $2 \sqrt{3}$ $8 \sqrt{3}$ 8

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

6
A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feer on the wall. Frod to the nearest degree, the angle the ladder makes with the wall. Round to the nearest whole number. Show all work for full credit. $\square$

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 the height of a stone face on a mountain, given angles of elevation of $28^{\circ}$ and $31^{\circ}$ from 800 feet away.

Find the value of $\csc (-1305)$ .

Find the second least positive value (in radians) for $\beta$ given $11\pi/6$ and for $\gamma$ given $\tan(\gamma)=1$ .

If $\tan (\gamma)=1$ , what are the least and second least positive values of $\gamma$ in radians?

Prove the trigonometric equation: $\theta \sin \left(\frac{1}{n}\right) \frac{x}{\sqrt{1-x^{2}}} = \tan^{-1}(x)$ .

Fing the angle of $D$

A calculator is allowed for this question. Solve for $x$ (round to the nearest thousandth)

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 $\frac{Z+1}{Z-1}=-i \cot \theta$