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