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Math Help - Inverse trig functions involving the unit circle?

  1. #1
    Member realintegerz's Avatar
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    Inverse trig functions involving the unit circle?

    How do I do these problems?

    1) cos ^ -1 ( cos (7 pi/4) )

    2) sin ^ -1 ( - sq. root 3 /2 )

    The answer to the first problem is supposed to be pi/4 and 7 pi/4
    but I don't get how to do these? I know our answers are to be in terms of the unit circle, so if you can explain it in detail please do so, and were not allowed to use a calculator to solve these

    I have no clue on how to do these inverse trig functions, I asked on yahoo answers and people weren't explaining well enough
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  2. #2
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    Quote Originally Posted by realintegerz View Post
    How do I do these problems?

    1) cos ^ -1 ( cos (7 pi/4) )

    2) sin ^ -1 ( - sq. root 3 /2 )

    The answer to the first problem is supposed to be pi/4 and 7 pi/4
    but I don't get how to do these? I know our answers are to be in terms of the unit circle, so if you can explain it in detail please do so, and were not allowed to use a calculator to solve these

    I have no clue on how to do these inverse trig functions, I asked on yahoo answers and people weren't explaining well enough
    From the definition of "inverse" cos^{-1}(cos(7\pi/4))= 7\pi/4 is the obvious solution (f^{-1} is defined by f^{-1}(f(x))= f(f^{-1}(x))= x). Since cosine is the x coordinate of a point on the unit circle, mark the point at angle 7\pi/4 which is in the 4th quadrant, at angle 2\pi- 7\pi/4= \pi/4 below the x-axis, and draw a vertical line there. You should be able to see by symmetry that the other point at which the line crosses the unit circle is at \pi/4 above the x-axis.
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