Question

How do you evaluate `tan^-1(0)` without a calculator?

Answer 1

`theta=0`

Explanation:

Find `tan^-1 (0)` without a calculator.

`tan^-1(0)` refers to the ANGLE whose tangent equals zero.

Recall the identity `tantheta = sintheta/costheta`

If `tantheta=0`, then the numerator of `sintheta/costheta` must also equal zero.

So, `sintheta"=0`.

Referring to the unit circle, the angles with a sine of zero are
`theta =0, pi`.

BUT, IT'S A BIT MORE COMPLICATED!

The range of `tan^-1` (also called arctan) is `-pi/2` to `pi/2`.

In other words, the only "allowed" values of `tan^-1` fall within this range. So, the the answer `theta=pi` is not allowed, and the answer to the problem `tan^-1(0)` is `theta=0`