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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
 #1
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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 = \(\frac{\sqrt{11}}{5}/-\frac{\sqrt{14}}{5}=\frac{\sqrt{11}}{5}\cdot-\frac{5}{\sqrt{14}}=-\frac{\sqrt{11}}{\sqrt{14}}=-\sqrt{\frac{11}{14}}\) 

 

*edit* made it for θ in the second quadrant.

hectictar  Apr 28, 2017
edited by hectictar  Apr 30, 2017

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