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Chapter 5: Problem 102
Use the sum-to-product formulas to find the exact value of the expression. $$\sin \frac{5 \pi}{4}-\sin \frac{3 \pi}{4}$$
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Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\sec ^{2} x+0.5 \tan x-1=0$$
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the given interval. $$3 \tan ^{2} x+5 \tan x-4=0, \quad\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$
Find the exact value of each expression. (a) \(\sin \left(\frac{3 \pi}{4}+\frac{5 \pi}{6}\right)\) (b) \(\sin \frac{3 \pi}{4}+\sin \frac{5 \pi}{6}\)
Determine whether the statement is true or false. Justify your answer. The equation \(2 \sin 4 t-1=0\) has four times the number of solutions in the interval \([0,2 \pi)\) as the equation \(2 \sin t-1=0\).
Find the exact value of the expression. $$\cos \frac{\pi}{16} \cos \frac{3 \pi}{16}-\sin \frac{\pi}{16} \sin \frac{3 \pi}{16}$$
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