Question

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)

Answer 1

(-√21,-2). option A.

Explanation:

Answer 2

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.