Question

How do you evaluate `tan(cos^-1(-2/3))` without a calculator?

Answer 1

`-sqrt 5/2`

Explanation:

Let `a = cos&(-1)(-2/3) in Q2`.

Tangent is negative in Q2, and sine is positive..

Now, `cos a =-2/3` and, the given expression is

`tan a = sin a/cos a.=sqrt(1-cos^2a)/cos a`

`=sqrt(1-(-2/3)^2)/(-2/3)`

`=-sqrt 5/2`