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21 March, 20:08

Find the exact value of sin (arccos (three fifths)). for full credit, explain your reasoning.

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  1. 21 March, 20:58
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    We want to evaluate sin (cos⁻¹ (3/5)).

    Note that

    sin²x + cos²x = 1

    Therefore

    sin²x = 1 - cos²x

    Let y = cos⁻¹ (3/5)

    Then

    cos (y) = 3/5

    sin²y = 1 - cos²y = 1 - 9/25 = 16/25

    sin (y) = 4/5

    Therefore

    sin (cos⁻¹ (3/5)) = sin (y) = 4/5

    Answer: 4/5
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