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Answer 1 · 2017-04-11T19:40:34

For part a. see below.

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.

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

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

$sectheta = 1/costheta = 13/12$

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