Question

How do you calculate the `arctan(0)`?

Answer 1

`arctan(0) = 0`

Explanation:

`arctan(0)` is at which at which x `tan(x) = 0`
and `-pi/2 < x < pi/2`
(or `-90 < x < 90` if you use degrees)

`tan(x) = sin(x)/cos(x)`
`tan(x) = 0`
when
`sin(x) = 0`

Use the attached unit circle from wikipedia:

`x = 0+n*2*pi`
or
`x = pi+n*2*pi`
so in this case
`x= n*pi`
where n is an integer
Only x = 0 satisfies
`-pi/2 < x < pi/2`

`sin(0)=0`
`tan(0)=0`
`arctan(0)=0`