# trig

If sin theta = 2/7 and theta is in quadrant 2 find cos theta, sec theta, csc theta, tan theta, and cot theta

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1. sin(Θ) = y/r

x = √(r^2 - y^2) = √(49 - 4) = √45 = 3√5

cos(Θ) = x/r ... sec(Θ) = r/x ... csc(Θ) = r/y ... tan(Θ) = y/x ... cot(Θ) = x/y

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2. careful with the sign.
x^2 + y^2 = r^2
x^2 + 4 = 49
x^2 = 45
x = ± 3√5
but since the angle is in quadrant II,
x = -3√5, y = 2 , r = 7

now sub into the formulas given by R_scott

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