Answer:
(-4.58, -2)
Step-by-step explanation:
[tex]\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[/tex]
Using Pythagoras Theorem
[tex]5^2=(-2)^2+ x^2\\25=4+x^2\\x^2=21\\x=\sqrt{21} \approx 4.58[/tex]
Since the angle is in the third Quadrant, Adjacent = -4.58.
Therefore, the coordinates of P(x,y) is (-4.58, -2)
