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

Solution:

As Given :

360° =  2 π Radians

π Radian = 180 °

degrees

Cosec ( theta) =

Let , Hypotenuse = - 5 k,  and Altitude = 2 k

By pythagorean theorem

Hypotenuse² =  Altitude² + Base²

(-5 k)²= (2 k)²  + Base²

25 k² - 4 k² = Base²

Base = 21 k²

Base = √21 k

Coordinates of P(x,y) = (-√21 : -2)

The answer is A

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