Chapter 5

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$\alpha=30^{\circ}, \quad b=20$$

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

Find the amplitude and the period and sketch the graph of the equation: A. \(y=4 \sin x\) B. \(y=\sin 4 x\) C. \(y=\frac{1}{4} \sin x\) D. \(y=\sin \frac{1}{4} x\) E. \(y=2 \sin \frac{1}{4} x\) F. \(y=\frac{1}{2} \sin 4 x\) G. \(y=-4 \sin x\) H. \(y=\sin (-4 x)\)

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. (a) \(240^{\circ}\) (b) \(340^{\circ}\) (c) \(-202^{\circ}\) (d)\(-660^{\circ}\)

Exer. 1-4: If the given angle is in standard position, find two positive coterminal angles and two negative coterminal angles. (a) \(120^{\circ}\) (b) \(135^{\circ} \quad\) (c) \(-30^{\circ}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$\beta=45^{\circ}, \quad b=35$$

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

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. (a) \(165^{\circ}\) (b) \(275^{\circ}\) (c)\(-110^{\circ}\) (d) \(400^{\circ}\)

Exer. 1-4: If the given angle is in standard position, find two positive coterminal angles and two negative coterminal angles. (a) \(240^{\circ} \quad\) (b) \(315^{\circ}\) \((c)-150^{a}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$\beta=45^{\circ}, \quad c=30$$

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=3 \cot x$$

Find the amplitude and the period and sketch the graph of the equation: A. \(y=3 \cos x\) B. \(y=\cos 3 x\) C. \(y=\frac{1}{3} \cos x\) D. \(y=\cos \frac{1}{3} x\) E. \(y=2 \cos \frac{1}{3} x\) F. \(y=\frac{1}{2} \cos 3 x\) G. \(y=-3 \cos x\) H. \(y=\cos (-3 x)\)

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. (a) \(3 \pi / 4\) (b) \(4 \pi / 3\) \((c)-\pi / 6\) \((d) 9 \pi / 4\)

Exer. 1-4: If the given angle is in standard position, find two positive coterminal angles and two negative coterminal angles. (a) \(620^{\circ}\) (b) \(\frac{5 \pi}{6} \quad\) (c) \(-\frac{\pi}{4}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$\alpha=60^{\circ}, \quad c=6$$

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=\frac{1}{3} \cot x$$

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. (a) \(7 \pi / 4\) (b) \(2 \pi / 3 \) (c) \(-3 \pi / 4\) \((d)-23 \pi / 6\)

Exer. 1-4: If the given angle is in standard position, find two positive coterminal angles and two negative coterminal angles. (a) \(570^{\circ}\) (b) \(\frac{2 \pi}{3}\) \((c)-\frac{5 \pi}{4}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$a=5, \quad b=5$$

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

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=\sin \left(x-\frac{\pi}{2}\right)\)

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. (a) 3 (b) \(-2\) \((c) 5.5\) (d) 100

Let \(P(t)\) be the point on the unit circle \(U\) that corresponds to \(t .\) If \(P(t)\) has the given rectangular coordinates, find (a) \(P(t+\pi)\) (b) \(P(t-\pi)\) (c) \(P(-t)\) (d) \(P(-t-\pi)\) $$\left(\frac{3}{5}, \frac{4}{5}\right)$$

Exer. \(5-6:\) Find the angle that is complementary to \(\theta\) (a) \(\theta=5^{\circ} 17^{\prime} 34^{\prime \prime}\) (b) \(\theta=32.5^{\circ}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$a=4 \sqrt{3}, \quad c=8$$

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

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

Find the reference angle \(\theta_{R}\) if \(\theta\) has the given measure. \((a) 6\) \((b)-4 \) \((c) 4.5\) \((d) \quad 80\)

Let \(P(t)\) be the point on the unit circle \(U\) that corresponds to \(t .\) If \(P(t)\) has the given rectangular coordinates, find (a) \(P(t+\pi)\) (b) \(P(t-\pi)\) (c) \(P(-t)\) (d) \(P(-t-\pi)\) $$\left(-\frac{8}{17}, \frac{15}{17}\right)$$

Exer. \(5-6:\) Find the angle that is complementary to \(\theta\) (a) \(\theta=63^{\circ} 4^{\prime} 15^{\prime \prime}\) (b) \(\quad \theta=82.73^{\circ}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$b=5 \sqrt{3}, \quad c=10 \sqrt{3}$$

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

Find the period and sketch the graph of the equation. Show the asymptotes. $$y=3 \sec x$$

Find the exact value. (a) \(\sin (2 \pi / 3)\) (b) \(\sin (-5 \pi / 4)\)

Let \(P(t)\) be the point on the unit circle \(U\) that corresponds to \(t .\) If \(P(t)\) has the given rectangular coordinates, find (a) \(P(t+\pi)\) (b) \(P(t-\pi)\) (c) \(P(-t)\) (d) \(P(-t-\pi)\) $$\left(-\frac{12}{13},-\frac{5}{13}\right)$$

Exer. \(7-8:\) Find the angle that is supplementary to \(\theta\) $$\text { (a) } \theta=48^{\circ} 51^{\prime} 37^{\prime \prime} \quad\left(\text { b) } \theta=136.42^{\circ}\right.$$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) find the exact values of the remaining parts. $$b=7 \sqrt{2}, \quad c=14$$

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

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

Find the exact value. (a) \(\sin 210^{\circ}\) (b) \(\sin \left(-315^{\circ}\right)\)

Let \(P(t)\) be the point on the unit circle \(U\) that corresponds to \(t .\) If \(P(t)\) has the given rectangular coordinates, find (a) \(P(t+\pi)\) (b) \(P(t-\pi)\) (c) \(P(-t)\) (d) \(P(-t-\pi)\) $$\left(\frac{7}{25},-\frac{24}{25}\right)$$

Exer. \(7-8:\) Find the angle that is supplementary to \(\theta\) $$\text { (a) } \theta=152^{\circ} 12^{\prime} 4^{\prime \prime} \quad \text { (b) } \theta=15.9^{\circ}$$

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$\alpha=37^{\circ}, \quad b=24$$

Find the amplitude, the period, and the phase shift and sketch the graph of the equation. \(y=\cos \left(x+\frac{\pi}{2}\right)\)

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

Find the exact value. (a) \(\cos 150^{\circ}\) (b) \(\cos \left(-60^{\circ}\right)\)

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) \(2 \pi \quad\) (b) \(-3 \pi\)

Exer. \(9-12:\) Find the exact radian measure of the angle. (a) \(150^{\circ}\) (b) \(-60^{\circ}\) (c) \(225^{\circ}\)

Given the indicated parts of triangle \(A B C\) with \(\gamma=90^{\circ},\) approximate the remaining parts. $$\beta=64^{\circ} 20^{\prime}, \quad a=20.1$$

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