Question 912184: Given sin theta = 21/29 and sec theta < 0, find tan theta and determine in which quadrant theta lies.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given sin theta = 21/29 and sec theta < 0, find tan theta and determine in which quadrant theta lies.
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sin is positive and sec negative in QII where x < 0 and y > 0
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By definition sin = y/r
Since sin = 21/29, y = 21 and r = 29
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Then x = -sqrt[29^2-21^2] = -sqrt(400) = -20
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sin = y/r = 21/29
cos = x/r = -20/29
tan = y/x = -21/20
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csc = 20/21
sec = -29/20
cot = -20/21
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Cheers,
Stan H.
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