Question

Question #7ce5f

Answer 1

For part a. see below.

Explanation:

Given: `sin theta = -5/13` and `(3pi)/2 < theta < 2pi`

We know that `sin^2theta+cos^theta=1` for all `theta`

Since `(3pi)/2 < theta < 2pi`, we see that `cos theta > 0`

Therefore,

`costheta = sqrt(1-sin^2theta) = sqrt (144/169) = 12/13`

Now we have

`sin theta = -5/13` and `costheta = 12/13`

The other values can be found using these two.

`tan theta = sintheta/costheta = -5/12`

`csc theta = 1/sintheta = -13/5`

`sectheta = 1/costheta = 13/12`

`cot theta = costheta/sintheta = -12/5`