How do you find the exact value of #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°#