SOLUTION: Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π. The circle's radius is 2.3 units long and the ter

Question 1180032: Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π. The circle's radius is 2.3 units long and the terminal point is (−1.35,1.86)
a) What is the slope of the terminal ray?
m=
b) Then, tan−1(m)=
c) Does the number we get in part (b) give us the correct value of θ? ? Yes No
d) Therefore, θ=

Answer by MathLover1(20855) (Show Source): You can put this solution on YOUR website!
The circle's radius is units long and the terminal point is (,)

the point (,) is in Q II and tan is negative
Since the position in the 3-o'clock is basically the positive x-axis, this means the angle that is terminating at (,) (which is in Q IV) should look like:
sketch

Notice that we can draw a right triangle by drawing a vertical straight line from the point (,).
from the right triangle we have

a) What is the slope of the terminal ray?

b) Then, °

c) Does the number we get in part (b) give us the correct value of ?

d) Therefore, since the point (,) is in Q II,
we then subtract it from because the coordinates of the point (,) are in the 4th quadrant, we need angle in Q II
°
°

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