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Chapter 5: Problem 47
Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\frac{\tan \theta \cot \theta}{\sec \theta}$$
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Use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$\csc ^{2} x+3 \csc x-4=0$$
Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{17 \pi}{12}=\frac{9 \pi}{4}-\frac{5 \pi}{6}$$
Find all solutions of the equation in the interval \([0,2 \pi)\). $$2 \sin ^{2} x+3 \sin x+1=0$$
Write the expression as the sine, cosine, or tangent of an angle. $$\sin 60^{\circ} \cos 15^{\circ}+\cos 60^{\circ} \sin 15^{\circ}$$
Determine whether the statement is true or false. Justify your answer. If you correctly solve a trigonometric equation to the statement \(\sin x=3.4\), then you can finish solving the equation by using an inverse function.
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