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Chapter 5: Problem 31
Use a double-angle formula to rewrite the expression. $$6 \cos ^{2} x-3$$
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Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$4 \sin ^{3} x+2 \sin ^{2} x-2 \sin x-1=0$$
Find the exact value of each expression. (a) \(\sin \left(135^{\circ}-30^{\circ}\right)\) (b) \(\sin 135^{\circ}-\cos 30^{\circ}\)
Use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$\csc ^{2} x-5 \csc x=0$$
(a) use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval \([0,2 \pi),\) and (b) solve the trigonometric equation and demonstrate that its solutions are the \(x\) -coordinates of the maximum and minimum points of \(f .\) (Calculus is required to find the trigonometric equation.) Function $$f(x)=\sin x \cos x$$ Trigonometric Equation $$-\sin ^{2} x+\cos ^{2} x=0$$
Write the expression as the sine, cosine, or tangent of an angle. $$\sin 60^{\circ} \cos 15^{\circ}+\cos 60^{\circ} \sin 15^{\circ}$$
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