SOLUTION: If theta is a third quadrant angle and cos theta= -2/3, find sin theta. Show work.

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Question 1138392: If theta is a third quadrant angle and cos theta= -2/3, find sin theta. Show work.
Found 3 solutions by MathLover1, Alan3354, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%28+theta%29=+-2%2F3
theta=cos%5E-1%28++-2%2F3%29
theta=131.8°->theta is a third quadrant angle
then
sin%28131.8%29=0.745476

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If theta is a third quadrant angle and cos theta= -2/3, find sin theta.
=-------------
sin = sqrt(1 - cos^2)
sine is negative in Q3

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

sin%28theta%29 = -sqrt%281+-+cos%5E2%28theta%29%29 = -sqrt%281+-+%28-2%2F3%29%5E2%29 = -sqrt%281+-+4%2F9%29 = -sqrt%285%2F9%29 = -sqrt%285%29%2F3.


The sign at the square root  is " - " (MINUS), because the angle theta is in QIII, by the condition.


It is your standard  "mantra",  which you should pronounce every time,  when you solve such a problem.