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Problem 34

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

Problem 34

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

Problem 34

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. $$\cot \left(-\frac{11 \pi}{6}\right)$$

Problem 35

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

Problem 35

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

Problem 35

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

Problem 36

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

Problem 36

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

Problem 36

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

Problem 37

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

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