Chapter 5

In Exercises \(21-32,\) graph the given function over one period. $$y=\cos (3 x)$$

In Exercises \(9-28,\) graph the functions over the indicated intervals. $$y=3 \cot \left(x-\frac{\pi}{6}\right),-\pi \leq x \leq \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\sin (-\pi)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-3 \cos \left(\frac{1}{2} x\right)$$

In Exercises \(9-28,\) graph the functions over the indicated intervals. $$y=\tan (2 x-\pi),-2 \pi \leq x \leq 2 \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\sin \left(-\frac{3 \pi}{2}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-2 \sin \left(\frac{1}{4} x\right)$$

In Exercises \(9-28,\) graph the functions over the indicated intervals. $$y=\cot (2 x-\pi),-2 \pi \leq x \leq 2 \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\sin \left(-\frac{\pi}{3}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-3 \sin (\pi x)$$

In Exercises \(9-28,\) graph the functions over the indicated intervals. $$y=\cot \left(\frac{x}{2}+\frac{\pi}{4}\right),-\pi \leq x \leq \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\cos \left(-\frac{\pi}{4}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-2 \cos (\pi x)$$

In Exercises \(9-28,\) graph the functions over the indicated intervals. $$y=\tan \left(\frac{x}{3}-\frac{\pi}{3}\right),-\pi \leq x \leq \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\cos \left(-\frac{3 \pi}{4}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=5 \cos (2 \pi x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=\sec \left(\frac{1}{2} x\right),-2 \pi \leq x \leq 2 \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\cos \left(-\frac{\pi}{2}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=4 \sin (2 \pi x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=\csc \left(\frac{1}{2} x\right),-2 \pi \leq x \leq 2 \pi$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\cos \left(-\frac{7 \pi}{6}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-3 \sin \left(\frac{\pi}{4} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=-\csc (2 \pi x),-1=x \leq 1$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\csc \left(-\frac{5 \pi}{6}\right)$$

In Exercises \(21-32,\) graph the given function over one period. $$y=-4 \sin \left(\frac{\pi}{2} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=-\sec (2 \pi x),-1 \leq x \leq 1$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\sec \left(-\frac{7 \pi}{4}\right)$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=-4 \cos \left(\frac{1}{2} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=\frac{1}{3} \sec \left(\frac{\pi}{2} x\right),-4 \leq x \leq 4$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\tan \left(-\frac{11 \pi}{6}\right)$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=-5 \sin \left(\frac{1}{2} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=\frac{1}{2} \csc \left(\frac{\pi}{3} x\right),-6 \leq x \leq 6$$

Use the unit circle and the fact that sine is an odd function and cosine is an even function to find the exact values of the indicated functions. $$\cot \left(-\frac{11 \pi}{6}\right)$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=-\sin (6 x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=-3 \csc \left(\frac{x}{3}\right),-6 \pi \leq x \leq 0$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cos \theta=\frac{\sqrt{3}}{2}, 0 \leq \theta \leq 2 \pi$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=-\cos (4 x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=-4 \sec \left(\frac{x}{2}\right),-4 \pi \leq x \leq 4 \pi$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cos \theta=-\frac{\sqrt{3}}{2}, 0 \leq \theta \leq 2 \pi$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=3 \cos \left(\frac{\pi}{4} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=2 \sec (3 x), 0 \leq x \leq 2 \pi$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sin \theta=-\frac{\sqrt{3}}{2}, 0 \leq \theta \leq 2 \pi$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=4 \sin \left(\frac{\pi}{4} x\right)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. $$y=2 \csc \left(\frac{1}{3} x\right),-3 \pi \leq x \leq 3 \pi$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sin \theta=\frac{\sqrt{3}}{2}, 0 \leq \theta \leq 2 \pi$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=\sin (4 \pi x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. \(y=-3 \csc \left(x-\frac{\pi}{2}\right)\), over at least none period

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sin \theta=0,0 \leq \theta \leq 4 \pi$$

In Exercises \(33-40,\) graph the given function over the interval \([-2 p, 2 p],\) where \(p\) is the period of the function. $$y=\cos (6 \pi x)$$

In Exercises \(29-46,\) graph the functions over the indicated intervals. \(y=5 \sec \left(x+\frac{\pi}{4}\right),\) over at least one period