Chapter 5

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec \pi$$

Compare the graph of the function with the graph of \(f(x)=\arctan x\) \(g(x)=-\arctan x-3\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=4 \sin x$$

Use the angle-conversion capabilities of a graphing utility to convert the angle measure to \(\mathbf{D}^{\circ} \mathbf{M}^{\prime} \mathbf{S}^{\prime \prime}\) form. $$-20.34^{\circ}$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\cot \frac{\pi}{2}$$

Compare the graph of the function with the graph of \(f(x)=\arctan x\) \(g(x)=\arctan (-x)+4\)

Use the graph of the function to determine whether the function is even, odd, or neither. \(f(x)=\cot 2 x\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=5 \sin x$$

Use the angle-conversion capabilities of a graphing utility to convert the angle measure to \(\mathbf{D}^{\circ} \mathbf{M}^{\prime} \mathbf{S}^{\prime \prime}\) form. $$45.063^{\circ}$$

Complete the identity. $$\sin ^{2} \theta+\cos ^{2} \theta=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec \frac{3 \pi}{2}$$

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\frac{1}{4} \cos x$$

Find (if possible) the complement and supplement of the angle. $$24^{\circ}$$

Complete the identity. $$1+\tan ^{2} \theta=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\csc 0$$

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\frac{3}{4} \cos x$$

Find (if possible) the complement and supplement of the angle. $$129^{\circ}$$

Find the angle \(\alpha\) between the two nonvertical lines \(L_{1}\) and \(L_{2}\) (assume \(L_{1}\) and \(L_{2}\) are not perpendicular). The angle \(\alpha\) satisfies the equation \(\tan \alpha=\left|\frac{m_{2}-m_{1}}{1+m_{2} m_{1}}\right|\) where \(m_{1}\) and \(m_{2}\) are the slopes of \(L_{1}\) and \(L_{2}\), respectively. $$\begin{aligned} &L_{1}: 3 x-2 y=5\\\ &L_{2}: \quad x+y=1 \end{aligned}$$

Complete the identity. $$\sin \left(90^{\circ}-\theta\right)=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\csc \frac{3 \pi}{2}$$

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. \(y_{1}=\sin x \sec x, \quad y_{2}=\tan x\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\cos \frac{x}{2}$$

Find (if possible) the complement and supplement of the angle. $$87^{\circ}$$

Find the angle \(\alpha\) between the two nonvertical lines \(L_{1}\) and \(L_{2}\) (assume \(L_{1}\) and \(L_{2}\) are not perpendicular). The angle \(\alpha\) satisfies the equation \(\tan \alpha=\left|\frac{m_{2}-m_{1}}{1+m_{2} m_{1}}\right|\) where \(m_{1}\) and \(m_{2}\) are the slopes of \(L_{1}\) and \(L_{2}\), respectively. $$\begin{aligned} &L_{1}: 2 x+y=8\\\ &L_{2}: \quad x-5 y=-4 \end{aligned}$$

Complete the identity. $$\cos \left(90^{\circ}-\theta\right)=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec 0$$

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. \(y_{1}=\frac{\cos x}{\sin x}, \quad y_{2}=\cot x\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\sin \frac{x}{4}$$

Find (if possible) the complement and supplement of the angle. $$167^{\circ}$$

Complete the identity. $$\tan \left(90^{\circ}-\theta\right)=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\cot \pi$$

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. \(y_{1}=1+\cot ^{2} x, \quad y_{2}=\csc ^{2} x\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\sin \left(x-\frac{\pi}{4}\right)$$

Complete the identity. $$\cot \left(90^{\circ}-\theta\right)=\square$$

Evaluate the trigonometric function of the quadrant angle, if possible. $$\csc \frac{\pi}{2}$$

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. \(y_{1}=\sec ^{2} x-1, \quad y_{2}=\tan ^{2} x\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\sin (x-\pi)$$

Complete the identity. $$\sec \left(90^{\circ}-\theta\right)=\square$$

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=120^{\circ}$$

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=-8 \cos (x+\pi)$$

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{\pi}{6}\) (b) \(\frac{5 \pi}{4}\)

Complete the identity. $$\csc \left(90^{\circ}-\theta\right)=\square$$

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=225^{\circ}$$

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=3 \cos \left(x+\frac{\pi}{2}\right)$$

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{5 \pi}{6}\) (b) \(-\frac{5 \pi}{3}\)

Use the function value(s) and the trigonometric identities to evaluate each trigonometric function. \(\sin 60^{\circ}=\frac{\sqrt{3}}{2}, \cos 60^{\circ}=\frac{1}{2}\) (a) \(\tan 60^{\circ}\) (b) \(\sin 30^{\circ}\) (c) \(\cos 30^{\circ}\) (d) \(\cot 60^{\circ}\)

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=150^{\circ}$$

Use the properties of inverse functions to find the exact value of the expression, if possible. cos(arccos 0.3)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=1-\sin \frac{2 \pi x}{3}$$

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{7 \pi}{4}\) (b) \(\frac{11 \pi}{4}\)