Given tantheta=5/12 and pi<theta<(3pi)/2, how do you find cos2theta?

1 Answer
Oct 28, 2016

cos2theta=119/169

Explanation:

Parametric formula for cosalpha
cosalpha=(1-t^2)/(1+t^2) where t=tan(alpha/2)

2theta=alpha, theta=alpha/2

cos2theta=(1-(5/12)^2)/(1+(5/12)^2)=119/169

5/12 < 1\ \ \ so \ \ \ pi < theta < 5/4pi

2pi < 2theta <5/2pi

0 < cos2theta < 1

119/169 is acceptable