Question

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)?

Answer 1

The answer is A

Explanation:

edge 2021

Answer 2

As Given :
`\pi <Theta <(3\pi)/(2)`

360° = 2 π Radians

π Radian = 180 °

`(3\pi )/(2) =270` degrees

Cosec ( theta) =
`(Hypotenuse )/(Perpendicular)=(-5)/(2)`

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)