Question

How do you find the exact value of `csc[arctan(-5/12)]`?

Answer 1

`-13/5`

Explanation:

Use definitions with respect to a right angled `triangle`ABC.
The hypotenuse of the right angled `triangle`ABC, with sides a and c including right angle B as 5 and 12, is 13.
`arctan (-5/12) = -arctan (5/12) = - arc csc (13/5)`.
csc arccsc (k) = k and csc(`-theta)=-csc(theta)`
So, the answer is `-13/5`.