Question

Sin theta = 1/4, tan theta > 0
Find cos theta/2

Answer 1

Explanation:

sin θ=1/4,tan θ>0

so θ lies in first quadrant.

cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4

`2cos^2 (\theta)/(2) =1+cos \theta`

`2~cos^2(\theta)/(2) =1+(√(15) )/(4) =(4+√(15))/(4) \\cos~(\theta)/(2) =\sqrt{(4+√(15) )/(4 * 2) } \\cos(\theta)/(2) =\frac{\sqrt{8+2√(15)} }{4}`