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Math Help - Use the identity cos^2(theta) + sin^2(theta) = 1

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    Use the identity cos^2(theta) + sin^2(theta) = 1

    Use the identity cos^2(θ) + sin^2(θ) = 1 to find sin(θ) when cos(θ) = 0.5

    Really lost on this. Is it something to do with the identities cos^2(x) = 1/2 + 1/2 cos(2x) and sin^2(x) = 1/2 - 1/2 cos(2x) ?

    Please provide a solution with steps.
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  2. #2
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    Lightbulb Re: Use the identity cos^2(theta) + sin^2(theta) = 1

    \pm \sqrt{1-0.5^2}
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    Re: Use the identity cos^2(theta) + sin^2(theta) = 1

    \cos^2 \theta + \sin^2 \theta = 1

    (0.5)^2 + \sin^2 \theta = 1

    \sin^2 \theta = 1 - 0.25

    \sin \theta = \pm \sqrt{0.75} = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}
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