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28 September, 01:17

Find the exact value of cos (arcsin (1/4)). For full credit, explain your reasoning.

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  1. 28 September, 01:39
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    First way

    arcsin (1/4) means that 1/4 sin of the angle.

    sin (α) = 1/4

    sin²α+cos²α=1

    (1/4) ²+cos²α=1

    cos²α=1-1/16 = 15/16

    cosα = + / - (√15) / 4

    Second way

    sin (α) = 1/4 = opposite leg/hipotenuse

    cos (α) = adjacent leg/hypothenuse

    adjacent leg = √ (hypotenuse² - Opposite²) = √ (16-1) = √15

    cosα=+/-√15/4

    For one value of sinα, possible 2 values of cosα.
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