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**+1 **

sin^{2}θ + cos^{2}θ = 1

(√11/5)^{2} + cos^{2}θ = 1

11/25 + cos^{2}θ = 1

cos^{2}θ = 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