Question

4. If the cosecant of a fourth quadrant angle is –π/e, what is its cosine? Thanks

Answer 1

`cos(theta) = sqrt(pi^2-e^2)/pi`

Explanation:

Since `csc(theta) = -pi/e`, we can use Pythagorean theorem to find the missing side in a `e, x, pi` triangle:

`x=sqrt(pi^2-e^2)`

So the ordered pair through which the angle passes is `(sqrt(pi^2-e^2), -e)`.

`cos(theta) = x/r = sqrt(pi^2-e^2)/pi`