SOLUTION: Dear Sir/Madam; A pleasant day! kindly help me in this Circular Functions problem: Find x so that P(x, -√13/4) lies on the unit circle in the third quadrant, find θ.

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Question 827226: Dear Sir/Madam;
A pleasant day! kindly help me in this Circular Functions problem:
Find x so that P(x, -√13/4) lies on the unit circle in the third quadrant, find θ.
Thank you very much for your help!

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find x so that P(x, -√(13)/4) lies on the unit circle
in the third quadrant, find θ.
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The radius is 1.
x is negative in the third quadrant
----
Equation:
Use Pythagoras to get:
x^2 + (sqrt(13)/4)^2 = 1
----
x^2 = 1-(13/16) = 3/16
x = -sqrt(3)/4
=====================
theta = arctan[(sqrt(13)/4)/(sqrt(3)/4)] = arctan(sqrt(13/3)) = 64.34 degrees
----
Solution in QIII:: 180+64.34 = 244.34 degrees
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Cheers,
Stan H.
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