Question

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

Answer 1

Answer: a

Step-by-step explanation: edge 2021

Answer 2

(-4.58, -2)

Explanation:

`\theta $ is in between \pi$ and $(3\pi)/(2)$ radians \\Therefore, \theta$ is in Quadrant III\\If \csc \theta = -(5)/(2)$ and cosec \theta = (Hypotenuse)/(Opposite) \\ $Therefore:\\Hypotenuse = 5\\Opposite $=-2`

Using Pythagoras Theorem

`5^2=(-2)^2+ x^2\\25=4+x^2\\x^2=21\\x=√(21) \approx 4.58`

Since the angle is in the third Quadrant, Adjacent = -4.58.

Therefore, the coordinates of P(x,y) is (-4.58, -2)