SOLUTION: find sin theta if cos theta=1/2 and theta terminates in quadrant IV

Question 831646: find sin theta if cos theta=1/2 and theta terminates in quadrant IV
Found 2 solutions by stanbon, KMST:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find sin theta if cos theta=1/2 and theta terminates in quadrant IV
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In QIV x is positive and y is negative
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Since cos = x/r, x = 1 and r = 2
Then y = -sqrt[2^2-1^2] = -sqrt(5)
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Ans: sin(t) = y/r = -sqrt(5)/2
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Cheers,
Stan H.
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Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For angles terminating in quadrant IV, sine is negative and cosine is positive.
For any angle , .
So, If ,

Since we know that ,
is not a solution.
The solution is

NOTE:
We also know that one of the possible values of is or ,
because a 30-60-90 right triangle (one with angles measuring 30, 60, and 90 degrees) is half of an equilateral triangle>

So for an equilateral triangle with side length of 1,
we get a right triangle where the leg opposite the angle (adjacent to the angle) measures ,
meaning that .
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