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:

(-4.58, -2)

Step-by-step explanation:

$\theta is in between \pi and \frac{3\pi}{2} radians \\Therefore, \theta is in Quadrant III\\If \csc \theta = -\dfrac{5}{2} and cosec \theta = \dfrac{Hypotenuse}{Opposite} \\ Therefore:\\Hypotenuse = 5\\Opposite =-2$

Using Pythagoras Theorem

$5^2=(-2)^2+ x^2\\25=4+x^2\\x^2=21\\x=\sqrt{21} \approx 4.58$

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

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