The point p(x, y) is on the terminal ray of angle theta. if theta is between pi radians and 3pi/2 radians and csc theta= -5/2, what are the coordinates of p(x, y)?
a. p(-sqr 21, -2)
b. p(sqr 21, -2)
c. p(-2, sqr 21)
d. p(-2, -sqr 21)

Csc(x) = 1/sin (x) = - 5/2 ⇒ sin (x) = - 2/5

sin(x) = opposite side / hypotenuse

If the opposite side measures 2 [this is the y-component, except for the sign]

hypotenuse measures 5, and the adyacent side is √(5^2 - 2^2) = √(25 - 4) = √21 [this is the x-component, except for the sign].

To assign the sign, we know that the quadrant between pi radians and 3Pi/2 radians is the third quadrant, where both the x-component and the y-component are negative.

Then the point is (-√21,-2). This is option A.