SOLUTION: If csc of theta is 3 and cos of theta is less than 0, find sin of theta, cos of theta, tan of theta, cot of theta and sec of theta

Question 573351: If csc of theta is 3 and cos of theta is less than 0, find sin of theta, cos of theta, tan of theta, cot of theta and sec of theta
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If csc of theta is 3 and cos of theta is less than 0,
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From that you can say that theta is in Q2 where x is negative and y is positive.
csc = r/y = 3/1 implies that r = 4 and y = 1
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Solve for "x":
r^2 = x^2 + y^2
4^2 = x^2 + 1
x^2 = 15
x = -sqrt(15) (because x is negative in Q2)
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find sin = y/r = 1/3
cos = x/r = -sqrt(15)/4
tan = y/x = -1/sqrt(15)
cot = x/y = -sqrt(15)
sec = r/x = -4/sqrt(15)
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Cheers,
Stan H.

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