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Math Help - Analytic Trig question 1

  1. #1
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    Analytic Trig question 1

    Find the exact value.

    18) cos[sin^-1(-(sqrt3)/2)]
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  2. #2
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    sqrt(3)/2 is a famous trigonometical value of some angle.

    cos^2(x) + sin^2(x) = 1 --> you can express cos with sin.
    And sin(sin^-1) is identic function, isn't it?
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  3. #3
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    so the angle value is 30 degrees. Does that mean the answer is [(sqrt3)/2], [1/2]?
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  4. #4
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    How have you gotten the first answer? The second is correct.
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  5. #5
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    The answer was derived from the graph using 30 degrees. What is the answer?
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  6. #6
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    Quote Originally Posted by kukid123 View Post
    Find the exact value.

    18) cos[sin^-1(-(sqrt3)/2)]
    Hi kukid123,

    Here is one way of doing it:

    \cos(\sin^{-1}(-\frac{\sqrt{3}}{2}))
    \sin^{-1}(-\frac{\sqrt{3}}{2})=180^0+60^0=240^0 or \sin^{-1}(-\frac{\sqrt{3}}{2})=360^0-60^0=300^0 Since sine is negative in the 3rd and 4th quadrants if 0<\theta<360^0.
    So \cos(\sin^{-1}(-\frac{\sqrt{3}}{2}))=\cos 240^0 = -\frac{1}{2} or \cos(\sin^{-1}(-\frac{\sqrt{3}}{2}))=\cos 300^0 = \frac{1}{2}
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