91Ó°ÊÓ

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. \(y_{1}=1+\cot ^{2} x, \quad y_{2}=\csc ^{2} x\)

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

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

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. \(y_{1}=\sec ^{2} x-1, \quad y_{2}=\tan ^{2} x\)

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

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

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

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

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