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Chapter 6: Problem 82
Use words to describe the formula for: the sine of double an angle.
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Describe a natural periodic phenomenon. Give an example of a question that can be answered by a trigonometric equation in the study of this phenomenon.
Without actually solving the equation, describe how to solve $$ 3 \tan x-2=5 \tan x-1 $$
Graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, this indicates that the equation is not an identity. In these exercises, find a value of \(x\) for which both sides are defined but not equal. $$ \sin \left(x+\frac{\pi}{2}\right)=\sin x+\sin \frac{\pi}{2} $$
Use a calculator to solve each equation, correct to four decimal places, on the interval \([0,2 \pi)\) $$ \tan ^{2} x-3 \tan x+1=0 $$
solve each equation on the interval \([0,2 \pi) .\) \(2 \sin ^{3} x-\sin ^{2} x-2 \sin x+1=0\) (Hint: Use factoring by grouping.)
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