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

1. ## 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?

2. Originally Posted by bloop
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.

3. Originally Posted by HallsofIvy
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?

4. $\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$ = ?

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### cos value for -1/root 2

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