SOLUTION: Find the exact value of each of the other 5 trigonometric functions for the angle of theta (without finding theta) when sine theta is -4/5 and cosine theta < 0

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Question 315191: Find the exact value of each of the other 5 trigonometric functions for the angle of theta (without finding theta) when sine theta is -4/5 and cosine theta < 0
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of each of the other 5 trigonometric functions for the angle of theta (without finding theta) when
sine theta is -4/5 and cosine theta < 0
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If cos(theta)<0 theta is in the 2nd or 3rd quadrant.
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If sin(theta) = -4/5 then y = -4 and r = 5
So now you know that theta is in the 3rd quadrant.
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x = sqrt(r^2-y^2) = sqrt(25-16) = 3
But theta is in the 3rd quadrant so x = -3
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sin = -4/5
cos = -3/5
tan = 4/3
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csc = -5/4
sec = -5/3
ctn = 3/4
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Cheers,
Stan H.