How do you find the exact value of cos^-1(-1/2)cos1(12)?

1 Answer
Aug 2, 2016

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

Explanation:

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°