# cos^-1frac{-1}{2}=

foass77W 2021-01-05 Answered
${\mathrm{cos}}^{-1}\frac{-1}{2}=$
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## Expert Answer

2abehn
Answered 2021-01-06 Author has 88 answers

The value of an inverse trig expression is an angle. ${\mathrm{cos}}^{-1}\frac{-1}{2}$ is then asking you what angle on the unit circle has a value of $\frac{-1}{2}$ for cosine.
Inverse cosine is restricted to the angles in the first and second quadrant. That is, inverse cosine can only equal an angle $oslash$ such that $0\le \theta \le \pi$  or  ${0}^{\circ }\le \theta \le {180}^{\circ }.$
Since cosine is the x-coordinate of the point on the unit circle, you need to look for what point in the first or second quadrant on the unit circle has an x-coordinate of $\frac{-1}{2}$. That point is
$\frac{-1}{2},\sqrt{\frac{3}{2}}$ in the second quadrant at an angle of $oslash=2\frac{\pi }{3}$ if your answer must be in radians and ${\mathrm{cos}}^{-1}\frac{-1}{2}={120}^{\circ }$ if your answer must be in degrees.

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