SOLUTION: If the terminal arm of angle θ intersects the unit circle at the point (−⅞,−√15⁄8) , then to the nearest hundredth of a radian, θ is

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Question 1181868: If the terminal arm of angle θ intersects the unit circle at the point
(−⅞,−√15⁄8) , then to the nearest hundredth of a radian, θ is
Found 2 solutions by greenestamps, Theo:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use your calculator.

The given point is in quadrant III (x, y both negative).

You have the lengths of all three sides of the triangle: x=7/8, y=sqrt(15)/8, r=1, so you can use inverse sine, inverse cosine, or inverse tangent to find the angle.

In any of those cases, your calculator won't give you an angle in quadrant III. So ignore the signs on the coordinates of the actual point -- i.e., use the point (7/8,sqrt(15)/8).

You have three choices for the computation to be made:

(1) sin%5E%28-1%29%28sqrt%2815%29%2F8%29
(2) cos%5E%28-1%29%287%2F8%29

(3) tan%5E%28-1%29%28sqrt%2815%29%2F7%29

All three of those calculations will give you an angle x in the first quadrant. Make sure your calculator is set to give you the answer in radians.

That angle x is the reference angle for the angle you are looking for; the angle you are looking for in quadrant III is (x+pi) radians.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the intersection with the unit circles is at (-7/8,-sqrt(15/8)
that means x = -7/8 and y = -sqrt(15/8)
the angle will be in the third quadrant.
to find the angle in the first quadrant, then find tan((7/8)/(sqrt(15/8)).
the trig function in the first quadrant is always positive.
the angle in the first quadrant will be arctan of that = .5053605103 radians.
the equivalent angle in the third quadrant will be that plus pi = 3.646953164 radians.
round that to the nearest hundredth of a radian makes it equal to 3.65 radians.

on a graph, that looks like this.



the angle that you're looking for is in quadrant 3.
the coordinate points are (3.647,.5533).
the angle is equal to 3.647 radians.
the tangent function is equal to .5533.
.5533 is equal to (sqrt(15)/8) / (7/8) .5532833352.
round that to 4 decimal places to get .5533.
that is what is shown on the graph.


on the unit circle, it looks like this.