Chapter 5

Find exact values of the given trigonometric functions without the use of a calculator. $$\arctan 1$$

Sketch the angles in standard position. $$210^{\circ}$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\sin x-2$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$\frac{11 \pi}{4}$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$g(x)=\cot \left(\frac{3 \pi}{4}+x\right)$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arccos \frac{1}{2}$$

Sketch the angles in standard position. $$-135^{\circ}$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$g(x)=\cos x-\frac{1}{2}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$ -\frac{7 \pi}{6} $$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$g(x)=\sec \left(\frac{\pi}{2}+x\right)$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arcsin \left(-\frac{1}{2}\right)$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$g(x)=\sin x+\frac{3}{2}$$

Sketch the angles in standard position. $$-225^{\circ}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$-\frac{5 \pi}{4}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$f(x)=4 \tan x$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\cos \left(x-\frac{\pi}{4}\right)$$

Sketch the angles in standard position. $$270^{\circ}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$\frac{3 \pi}{4}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$f(x)=-3 \tan x$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\sin (x+\pi)$$

Sketch the angles in standard position. $$450^{\circ}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$\frac{4 \pi}{3}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$f(x)=2 \csc x$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\tan ^{-1}(-\sqrt{3})$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$g(x)=\cos \left(\frac{3 \pi}{4}+x\right)$$

Sketch the angles in standard position. $$\frac{7 \pi}{4}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$-\frac{5 \pi}{6}$$

Use the given value of a trigonometric function of \(\theta\) to find the values of the other five trigonometric functions. Assume \(\theta\) is an acute angle. $$\cos \theta=\frac{3}{5}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$f(x)=3 \sec x$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$g(x)=\sin \left(\frac{5 \pi}{4}+x\right)$$

Sketch the angles in standard position. $$\frac{5 \pi}{3}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$-\frac{7 \pi}{4}$$

Use the given value of a trigonometric function of \(\theta\) to find the values of the other five trigonometric functions. Assume \(\theta\) is an acute angle. $$\sin \theta=\frac{12}{13}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$g(x)=-2 \cot x$$

Use a calculator to evaluate each trigonometric function. Make sure that the calculator is in \(R A D I A N\) mode. $$\arcsin \left(-\frac{1}{4}\right)$$

Use your knowledge of vertical stretches and compressions to graph at least two cycles of the given functions. $$f(x)=-2 \sin x$$

Sketch the angles in standard position. $$\frac{9 \pi}{4}$$

Skills This set of exercises will reinforce the skills illustrated in this section. Find the reference angle for each of the angles given. $$225^{\circ}$$

Use the given value of a trigonometric function of \(\theta\) to find the values of the other five trigonometric functions. Assume \(\theta\) is an acute angle. $$\tan \theta=\frac{3}{2}$$

Use your knowledge of vertical stretches to graph at least two cycles of the given functions. $$g(x)=-3 \csc x$$

Use a calculator to evaluate each trigonometric function. Make sure that the calculator is in \(R A D I A N\) mode. $$\arccos \left(-\frac{1}{5}\right)$$

Use your knowledge of vertical stretches and compressions to graph at least two cycles of the given functions. $$f(x)=-3 \cos x$$

Sketch the angles in standard position. $$\frac{8 \pi}{3}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$-150^{\circ}$$

Use the given value of a trigonometric function of \(\theta\) to find the values of the other five trigonometric functions. Assume \(\theta\) is an acute angle. $$\tan \theta=\frac{1}{2}$$

Use your knowledge of horizontal stretches and compressions to graph at least two cycles of the given functions. $$f(x)=\tan (2 x)$$

Use a calculator to evaluate each trigonometric function. Make sure that the calculator is in \(R A D I A N\) mode. $$\arccos 0.75$$