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Question
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
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Solution
Given: sinθ = `8/17`
We know that sin2θ + cos2θ = 1
∴ cos2θ = 1 - sin2θ
∴ cos θ = `sqrt(1 - sin^2θ)`
Using given
`cosθ = sqrt(1 - (8/17)^2) = sqrt(1 - 8^2/17^2)`
∴ cos θ = `sqrt((17^2 - 8^2)/17^2) = sqrt(289 - 64)/17`
∴ cos θ = `sqrt(225)/17 = 15/17`
∴ cos θ = `15/17`
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