How do you find the exact value of ${cos}^{- 1} (- \frac{1}{2})$ $cos^-1(-1/2)$ ?

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Answer 1 · 2016-08-02T20:59:02

For $0<= theta<=360°$ , $theta = 120°or 240°$

$cos 60° = 1/2$

This is one of the special angles which we should know and recognize.

Hence $Cos^-1(1/2) = 60°$

However in this case we are working with $(-1/2)$

From the "CAST" rule, we find that cos is negative in the second and third quadrants.

In the second quadrant, use $180-theta$ .
In the third use $180+theta$ .

From 0° to 360° there are two values of theta for
$theta = Cos^-1(-1/2)$

$theta = 180-60 = 120°$

$theta = 180+60=240°$

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