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Math Help - cos x = -1 / sqrt(2) without a calculator

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    cos x = -1 / sqrt(2) without a calculator

    hey my teacher requires us to be able to evaluate arcsines and arccosines and arctangents without a calculator (exact values). I know how to do it with the unit circle points (pi/4, pi/3, etc.) but not with other, random values. Can anyone help?
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  2. #2
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    Quote Originally Posted by bloop View Post
    hey my teacher requires us to be able to evaluate arcsines and arccosines and arctangents without a calculator (exact values). I know how to do it with the unit circle points (pi/4, pi/3, etc.) but not with other, random values. Can anyone help?
    You can't! Not with random values and I am sure your teacher does not expect you to find, say cos^{-1}(3/5). As far as this particular question, cos(x)= -1/\sqrt{2}, if, as you say, you know "(pi/4, pi/3, etc.)" then this should be easy. cos(t) is the x coordinate of a point on the unit circel so draw a vertical line at x= -1/\sqrt{2} and think about the symmetry of the circle.
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    Quote Originally Posted by HallsofIvy View Post
    You can't! Not with random values and I am sure your teacher does not expect you to find, say cos^{-1}(3/5). As far as this particular question, cos(x)= -1/\sqrt{2}, if, as you say, you know "(pi/4, pi/3, etc.)" then this should be easy. cos(t) is the x coordinate of a point on the unit circel so draw a vertical line at x= -1/\sqrt{2} and think about the symmetry of the circle.
    ok i get it now, and this is a really stupid question, but why does 1/sqrt(2) = sqrt (2) / 2?
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    \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = ?
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