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# If sin (theta) = √11/5 and theta is in the 2nd quadrant, find the exact values (without a calculator) of:

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If sin (theta) = √11/5 and theta is in the 2nd quadrant, find the exact values (without a calculator) of:

Cos (theta)
Tan (theta)

Guest Apr 28, 2017
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sin2θ + cos2θ = 1

(√11/5)2 + cos2θ = 1

11/25 + cos2θ = 1

cos2θ = 1 - 11/25

cos θ = $$-\sqrt{\frac{14}{25}}=-\frac{\sqrt{14}}{5}$$

tan θ = sin θ / cos θ

tan θ = $$\frac{\sqrt{11}}{5}/-\frac{\sqrt{14}}{5}=\frac{\sqrt{11}}{5}\cdot-\frac{5}{\sqrt{14}}=-\frac{\sqrt{11}}{\sqrt{14}}=-\sqrt{\frac{11}{14}}$$