The value of an inverse trig expression is an angle. cos−1−12 is then asking you what angle on the unit circle has a value of −12 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≤θ≤π or 0∘≤θ≤180∘. 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 −12. That point is −12,32 in the second quadrant at an angle of oslash=2π3 if your answer must be in radians and cos−1−12=120∘ if your answer must be in degrees.

Expert Answer to "cos−1−12="

foass77W

Answered question

2021-01-05

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

Answer & Explanation

2abehn

Skilled2021-01-06Added 88 answers

The value of an inverse trig expression is an angle. $\cos^{- 1} \frac{- 1}{2}$ 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 $o s l a s h$ such that $0 \leq θ \leq π$ or $0^{\circ} \leq θ \leq 180^{\circ} .$
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 $o s l a s h = 2 \frac{π}{3}$ if your answer must be in radians and $\cos^{- 1} \frac{- 1}{2} = 120^{\circ}$ if your answer must be in degrees.

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