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27 May, 12:40

Fatima wants to find the value of sin 0 given cot 0 = 4/7 which identity should she use

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  1. 27 May, 13:38
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    The cot (theta) = 4/7

    That means we have an adjacent of 4 and an opposite of 7. We still need to find the hypotenuse.

    Step One

    Find the hypotenuse

    a^2 + b^2 = c^2

    a = 4

    b = 7

    c = ?

    4^2 + 7^2 = c^2

    c^2 = 16 + 49

    c^2 = 65 Take the square root of both sides.

    c = sqrt (65)

    Now find Sin (theta)

    Sin (theta) = 7 / sqrt (65)

    The other way to do it would be to solve

    cot^2 (theta) + 1 = csc^2 (theta)

    (4/7) ^2 + 1 = csc^2 (theta)

    16/49 + 1 = csc^2 (theta)

    65/49 = csc^2 (theta)

    sqrt (65) / 7 = csc (theta)

    7 / sqrt (65) = sin (theta)

    There's a choice of two ways to do it. The first way is using cot = adjacent / opposite.

    The second is using

    1 + cot^2 (theta) = csc^2 (theta) and

    sin (theta) = 1 / csc (theta).
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