Find the value for θ. sinθ=cos(θ−18.5)

Question

Find the value for θ.

sinθ=cos(θ−18.5)

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Bella 2 weeks 2021-09-12T09:34:12+00:00 1 Answer 0

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    2021-09-12T09:36:00+00:00

    Answer:

    \theta=54.25 in the interval 0\leq\theta\leq90°

    Step-by-step explanation:

    I assume the angles are in degrees and the interval is from 0 to 90 degrees.

    Given:

    \sin \theta=\cos(\theta-18.5)

    We know that,

    \sin \theta=\cos(90-\theta)

    Therefore, replace \sin \theta by \cos(90-\theta), we get:

    \cos(90-\theta)=\cos(\theta-18.5)

    90-\theta=\theta-18.5\\90+18.5=\theta+\theta\\108.5=2\theta\\\theta=\frac{108.5}{2}=54.25

    Therefore, the value of \theta=54.25

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