Answer:
A. P(-sqr 21, -2)
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.