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2 votes
Given cosx = 60/61, find sin2x

User Xeos
by
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1 Answer

5 votes

Recall that for all x,

cos²(x) + sin²(x) = 1

So we have

sin(x) = ± √(1 - (60/61)²) = ± 11/61

Recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

From here, we get

sin(2x) = 2 (± 11/61) (60/61) = ± 1320/3721

In case you meant to ask about sin²(x), we get

sin²(x) = 1 - cos²(x) = 121/3721

User Maciej S
by
8.0k points

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