Given that $\cos 2 α = \frac{4}{5}$ and $α$ terminates in quadrant I, find the exact value of $\sin α$
$\sin α =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

Thus, the exact value of $\sin α$ is $0.316227766016838$ .

Steps

Step 1 ：We are given that $\cos 2 α = \frac{4}{5}$ and $α$ is in quadrant I.

Step 2 ：We can use the double angle formula for cosine, which is $\cos 2 α = 1 - 2 \sin^{2} α$ .

Step 3 ：Setting this equal to $\frac{4}{5}$ , we get the equation $1 - 2 \sin^{2} α = \frac{4}{5}$ .

Step 4 ：Solving this equation for $\sin α$ , we get two solutions: $- 0.316227766016838$ and $0.316227766016838$ .

Step 5 ：Since $α$ is in quadrant I, where sine is positive, we discard the negative solution.

Step 6 ：Thus, the exact value of $\sin α$ is $0.316227766016838$ .