Question

The point P(x, y) is on the terminal ray of angle theta. If theta is between pi radians and 3pi/2 radians and csc theta= -5/2, what are the coordinates of P(x, y)?
A. P(-sqr 21, -2)B. P(sqr 21, -2)C. P(-2, sqr 21)D. P(-2, -sqr 21)

Answer 1

Answer:

A on E2020.

Step-by-step explanation:

Answer 2

Answer:

A. P(-sqr 21, -2)

Step-by-step explanation:

Given

csc theta= -5/2

means that

sin theta= -2/5

theta = arcsin(-2/5 )

theta = -23.578°

Sine is a periodic function, so there are two theta values which satisfy sin theta= -2/5, those are:

theta = 360° - 23.578° = 336.422°

theta = 180° + 23.578° = 203.578°

Given that theta is between pi radians (180°) and 3pi/2 radians (270°), then theta = 203.578°.

The angle formed by a point P(x,y)with the x-axis is calculated as follows:

alpha = arctan(y/x)

For P(-sqr 21, -2):

alpha = arctan(-2/-sqr 21) = 23.578°

The point P(-sqr 21, -2) is located in the third quadrant, that is, between 180° and 270°, then 23° is the angle between the point and the negative x-axis, the aforementioned theta measures the angle respect positive x-axis, therefore alpha and theta are equivalent.