Question

If theta is between pi radians and 3pi/2 radians and csc= -5/2, what are the coordinates of x and y

Answer 1

(-√29, -2)

Explanation:

This angle is in Quadrant III, and so the opp side is -, the adj side is also -, and opp² + adj² = hyp².

Here we have csc Ф = 5/(-2) = hyp / opp.

The hyp has length 5, the opp side has length 2, and the adj side has length √(5²+2²), or √29

With y = -2 and x = -√29, the coordinates x and y are (-√29, -2). Yes, this is in Quadrant III.