Question

How do you evaluate `tan(arccos(-3/4))` without a calculator?

Answer 1

`-sqrt 7/3`

Explanation:

Let `a = arc cos (-3/4) in Q2`, wherein tangent is also negative.

Then, the given expression is

`tan a = sin a/cos a=-sqrt(1-(-3/4)^2)/(-3/4)=-sqrt 7/3`