Question

What is `tan(-9pi)`?

Answer 1

`tan(-9pi)=color(green)(0)`

Explanation:

When evaluating angles (specified in radians) any angle `theta` is equivalent to `theta+2kpi` for `kin ZZ` since an angle of `2pi` represents a complete circle.

So when evaluating `tan(-9pi)` we can equate
`color(white)("XXX")-9pi = -7pi=-5pi=-3pi=-pi=pi`

That is
`color(white)("XXX")tan(-9pi)=tan(pi)`

Using the unit circle and an angle in standard position,
the angle `pi` is a point on the negative X-axis at `(x,y)=(-1,0)`

`rArr tan(-9pi) = y/x = 0/(-1) = 0`