Question

How do you evaluate `cos^-1(1/2)` without a calculator?

Answer 1

`cos^(-1)(-1/2)=120^@`

Explanation:

See from tables relating to trigonometric ratios of special angles ass shown in figure below

we have `cos120^@=-1/2` and `cos240^@=-1/2`

However range for `theta=cos^(-1)x` is `0 < theta < pi`

Hence, `cos^(-1)(-1/2)=120^@`.