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Magazine Problem 47
Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\csc \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$
Problem 48
In Exercises \(47-56,\) graph the functions over at least one period. $$y=-3+2 \csc \left(x+\frac{\pi}{2}\right)$$
Problem 48
Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\sec \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$
Problem 49
Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\tan \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$
Problem 49
In Exercises \(47-56,\) graph the functions over at least one period. $$y=\frac{1}{2}+\frac{1}{2} \tan \left(x-\frac{\pi}{2}\right)$$
Problem 49
In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=2 \sin (\pi x-1)$$
Problem 50
In Exercises \(47-56,\) graph the functions over at least one period. $$y=\frac{3}{4}-\frac{1}{4} \cot \left(x+\frac{\pi}{2}\right)$$
Problem 50
In Exercises \(49-60\), state the amplitude, period, and phase shift (including direction) of the given function. $$y=4 \cos (x+\pi)$$
Problem 50
Use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$\cot \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi$$
Problem 51
In Exercises \(47-56,\) graph the functions over at least one period. $$y=-2+3 \csc (2 x-\pi)$$
