Chapter 5

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sin \theta=-1,0 \leq \theta \leq 4 \pi$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cos \theta=-1,0 \leq \theta \leq 4 \pi$$

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

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

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\tan \theta=-1,0 \leq \theta \leq 2 \pi$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cot \theta=1,0 \leq \theta \leq 2 \pi$$

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

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

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

In Exercises \(47-56,\) graph the functions over at least one period. $$y=3-2 \sec \left(x-\frac{\pi}{2}\right)$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\csc \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-3+2 \csc \left(x+\frac{\pi}{2}\right)$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sec \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=2 \sin (\pi x-1)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=\frac{1}{2}+\frac{1}{2} \tan \left(x-\frac{\pi}{2}\right)$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\tan \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=4 \cos (x+\pi)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=\frac{3}{4}-\frac{1}{4} \cot \left(x+\frac{\pi}{2}\right)$$

Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cot \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=-5 \cos (3 x+2)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-2+3 \csc (2 x-\pi)$$

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

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=-7 \sin (4 x-3)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-1+4 \sec (2 x+\pi)$$

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

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=6 \sin [-\pi(x+2)]$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-1-\sec \left(\frac{1}{2} x-\frac{\pi}{4}\right)$$

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

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=3 \sin \left[-\frac{\pi}{2}(x-1)\right]$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-2+\csc \left(\frac{1}{2} x+\frac{\pi}{4}\right)$$

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

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=3 \sin (2 x+\pi)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-2-3 \cot \left(2 x-\frac{\pi}{4}\right),-\pi \leq x \leq \pi$$

Refer to the following: The average daily temperature in Peoria, Illinois, can be predicted by the formula \(T=50-28 \cos \left[\frac{2 \pi(x-31)}{365}\right],\) where \(x\) is the number of the day in the year (January \(1=1\), February \(1=32\), etc.) and \(T\) is in degrees Fahrenheit.

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=-4 \cos (2 x-\pi)$$

In Exercises \(47-56,\) graph the functions over at least one period. $$y=-\frac{1}{4}+\frac{1}{2} \sec \left(\pi x+\frac{\pi}{4}\right),-2 \leq x \leq 2$$

Refer to the following: The average daily temperature in Peoria, Illinois, can be predicted by the formula \(T=50-28 \cos \left[\frac{2 \pi(x-31)}{365}\right],\) where \(x\) is the number of the day in the year (January \(1=1\), February \(1=32\), etc.) and \(T\) is in degrees Fahrenheit. Atmospheric Temperature. What is the expected temperature on August \(15 ?\) (Assume it is not a leap year.)

In Exercises \(57-66,\) state the domain and range of the functions. $$y=\tan \left(\pi x-\frac{\pi}{2}\right)$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=-\frac{1}{4} \cos \left(\frac{1}{4} x-\frac{\pi}{2}\right)$$

Refer to the following: The human body temperature normally fluctuates during the day. A person's body temperature can be predicted by the formula \(T=99.1-0.5 \sin \left(x+\frac{\pi}{12}\right),\) where \(x\) is the number of hours since midnight and \(T\) is in degrees Fahrenheit. What is the person's temperature at \(6.00 \mathrm{A} \cdot \mathrm{M} . ?\)

In Exercises \(57-66,\) state the domain and range of the functions. $$y=\cot \left(x-\frac{\pi}{2}\right)$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=\frac{1}{2} \sin \left(\frac{1}{3} x+\pi\right)$$

In Exercises \(57-66,\) state the domain and range of the functions. $$y=2 \sec (5 x)$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=2 \cos \left[\frac{\pi}{2}(x-4)\right]$$

Refer to the following: The height of the water in a harbor changes with the tides. The height of the water at a particular hour during the day can be determined by the formula \(h(x)=5+4.8 \sin \left[\frac{\pi}{6}(x+4)\right]\) where \(x\) is the number of hours since midnight and \(h\) is the height of the tide in feet. What is the height of the tide at 3.00 P.M.? (IMAGE CANNOT COPY)

In Exercises \(57-66,\) state the domain and range of the functions. $$y=-4 \sec (3 x)$$

In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=-5 \sin [-\pi(x+1)]$$

Refer to the following: The height of the water in a harbor changes with the tides. The height of the water at a particular hour during the day can be determined by the formula \(h(x)=5+4.8 \sin \left[\frac{\pi}{6}(x+4)\right]\) where \(x\) is the number of hours since midnight and \(h\) is the height of the tide in feet. What is the height of the tide at 5.00 A.M.?

In Exercises \(57-66,\) state the domain and range of the functions. $$y=2-\csc \left(\frac{1}{2} x-\pi\right)$$

In Exercises \(61-66,\) sketch the graph of the function over the indicated interval. $$y=\frac{1}{2}+\frac{3}{2} \cos (2 x+\pi),\left[-\frac{3 \pi}{2}, \frac{3 \pi}{2}\right]$$