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28 January, 12:08

Find the value for sin (θ) if the following conditions hold: cos (2 theta) = 3/4 and 270 degrees

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  1. 28 January, 14:35
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    sin (θ) = - 0.35355

    Step-by-step explanation:

    The second condition is

    270 degrees
    cos (2*theta) = 3/4

    And we know the relation

    cos (2*θ) = 1-2sin^2 (θ)

    This means that,

    sin^2 (θ) = 0.5 * (1-cos (2*θ))

    sin (θ) = ± √ (0.5 * (1-cos (2*θ)))

    sin (θ) = ± √ (0.125)

    sin (θ) = ± 0.35355

    But we are in the 4th quadrant.

    This means that the sine is negative.

    sin (θ) = - 0.35355
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