How do you evaluate $cot(arcsin(-5/8)$ ?

Question

4100 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-22T01:20:42

Let $t=arcsin(-5/8)$

Then $t$ is in $[- pi/2, pi/2]$ and $sint = -5/8$

Find $cost$ (I'm sure you have done this kind of problem by now.)

Because $-pi/2 < t < pi/2$ , we know that $cost > 0$

$cost = sqrt39 / 8$

And $cot t = cost/sint =- sqrt39 / 5$

Method 2

Use $cot^2t =csc^2t -1$ together with $-pi/2 < t < pi/2$ , so we know that $cos t > 0$ and so $cot t < 0$

$csc t = -8/5$ , so $cot^2t =(-8/5)^2 -1 = 39/25$ and so on

How do you evaluate cot(arcsin(-5/8)cot(arcsin(-5/8)?