Chapter 5

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\tan \left(x+\frac{\pi}{2}\right)$$

Find the exact value. (a) \(\cos (5 \pi / 4) \) (b) \(\cos (-11 \pi / 6)\)

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(-\pi\) (b) \(6 \pi\)

Exer. \(9-12:\) Find the exact radian measure of the angle. (a) \(120^{\circ}\) (b)-135^{0}\( (c) \)210^{\circ}$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$\beta=71^{\circ} 51^{\prime}, \quad b=240.0$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=4 \cos \left(x-\frac{\pi}{4}\right)\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\tan 2 x$$

Find the exact value. (a) \(\tan (5 \pi / 6)\) (b) \(\tan (-\pi / 3)\)

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(3 \pi / 2 \quad\) (b) \(-7 \pi / 2\)

Exer. \(9-12:\) Find the exact radian measure of the angle. (a) \(450^{\circ}\) (b) \(72^{\circ}\) (c) \(100^{\circ}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$\alpha=31^{\circ} 10^{\prime}, \quad a=510$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=3 \cos \left(x+\frac{\pi}{6}\right)\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\tan \frac{1}{2} x$$

Find the exact value. (a) \(\tan 330^{\circ}\) (b) \(\tan \left(-225^{\circ}\right)\)

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(5 \pi / 2\) \((0)-\pi / 2\)

Exer. \(9-12:\) Find the exact radian measure of the angle. $$\begin{array}{llll} \text { a) } 630^{\circ} & \text { (b) } 54^{\circ} & \text { (c) } 95^{\circ} \end{array}$$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$a=25, \quad b=45$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=3 \cos \left(x+\frac{\pi}{6}\right)\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\tan \frac{1}{4} x$$

Find the exact value. (a) \(\cot 120^{\circ}\) (b) \(\cot \left(-150^{\circ}\right)\)

Exer. \(13-16:\) Find the exact degree measure of the angle. (a) \(\frac{2 \pi}{3}\) (b) \(\frac{11 \pi}{6} \quad\) (c) \(\frac{3 \pi}{4}\)

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(9 \pi / 4 \quad\) (b) \(-5 \pi / 4\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$a=31, \quad b=9.0$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=-\sin (3 x+\pi)-1\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\tan 4 x$$

Find the exact value. (a) \(\cot (3 \pi / 4)\) (b) cot \((-2 \pi / 3)\)

Exer. \(13-16:\) Find the exact degree measure of the angle. $$\begin{array}{cccc} (\mathrm{a}) \frac{5 \pi}{6} & (\mathrm{b}) \frac{4 \pi}{3} & (\mathrm{c}) \frac{11 \pi}{4} \end{array}$$

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(3 \pi / 4\) \((b)-7 \pi / 4\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$c=5.8, \quad b=2.1$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=-\cos (3 x+\pi)-2\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=2 \tan \left(2 x+\frac{\pi}{2}\right)$$

Find the exact value. (a) \(\sec (2 \pi / 3)\) (b) \(\sec (-\pi / 6)\)

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. $$5 \pi / 4 \quad(0)-\pi / 4$$

Exer. \(13-16:\) Find the exact degree measure of the angle. $$\text { (a) }-\frac{7 \pi}{2} \quad \text { (b) } 7 \pi \quad \text { (c) } \frac{\pi}{9}$$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$a=0.42, \quad c=0.68$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=\cos (2 x-\pi)+2\)

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\frac{1}{3} \tan \left(2 x-\frac{\pi}{4}\right)$$

Find the exact value. (a) sec \(135^{\circ}\) (b) \(\sec \left(-210^{\circ}\right)\)

Exer. \(13-16:\) Find the exact degree measure of the angle. $$\text { (a) }-\frac{5 \pi}{2} \quad \text { (b) } 9 \pi \quad \text { (c) } \frac{\pi}{16}$$

Let \(P\) be the point on the unit circle \(U\) that corresponds to \(t .\) Find the coordinates of \(P\) and the exact values of the trigonometric functions of \(t,\) whenever possible. (a) \(7 \pi / 4\) (b) \(-3 \pi / 4\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) express the third part in terms of the first two. $$\alpha, c ; \quad b$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=-2 \sin (3 x-\pi)\)

Use a formula for negatives to find the exact value. $$\text { (a) } \sin \left(-90^{\circ}\right) \quad \text { (b) } \cos \left(-\frac{3 \pi}{4}\right) \quad \text { (c) } \tan \left(-45^{\circ}\right)$$

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=-\frac{1}{4} \tan \left(\frac{1}{2} x+\frac{\pi}{3}\right)$$

Find the exact value. (a) cse \(240^{\circ}\) (b) \(\csc \left(-330^{\circ}\right)\)

Find the exact values of the trigonometric functions for the acute angle \(\theta\). $$\sin \theta=\frac{3}{5}$$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) express the third part in terms of the first two. $$\beta, c ; \quad b$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=3 \cos (3 x-\pi)\)

Use a formula for negatives to find the exact value. $$\text { (a) } \sin \left(-\frac{3 \pi}{2}\right) \quad \text { (b) } \cos \left(-225^{\circ}\right) \quad \text { (c) } \tan (-\pi)$$

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=-3 \tan \left(\frac{1}{3} x-\frac{\pi}{3}\right)$$