Evaluate arccos (-1/2)

Question

arccos(-1/2)

Answer 1

You want x such that cos(x) = -1/2

 

That puts x in the left half-plane, and it can be 60° above the -x axis or 60° below the -x axis, since cos60° = 1/2.  That gives you 2 values:

 

x = 120° or 240°

Answer 2

This problem just means what angle (in first or second quadrants) has its cosine value = negative one half?

 

The answer is 120 degrees, or 2pi/3 radians