Question

How do you find the `csc` of `theta` if `cottheta=1` and `pi<theta<3/2pi`?

Answer 1

`theta=0`

Explanation:

`cottheta=1:.tantheta=1`

`theta=tan^-1(1)=(pi/4)^"c"`

However, the given range is between `pi` and `3/2pi`, so this value cannot be used.

In order to find the value permissible within the range, we just need to add `pi` to the principle value of `theta` to get the actual value needed.

So the value of `theta` within the given range is `5/4pi`

`csctheta=1/sintheta=1/sin(5/4pi)=1/-0.707=-1.41`