Trig
posted by Waldo on .
Find all values of theta in the interval 0 <= theta < 360 that satisfy the equation 3cos(2theta)=7cos(theta). Express answers to the nearest ten minutes.

Cos2T= sin^2TCos^2T=12cos^2T
36cos^2T=7cosT
let u=cosT
6u^2+7u3=0
(3u1)(2u+3)=0
u= 1/3 u= 2/3
so what angles are those? 
3cos(2Ø)=7cos(Ø)
3(2cos^2 Ø  1) = 7cosØ
6cos^ Ø  7cosØ  3 = 0
(3cosØ+1)(2cosØ3) = 0
cosØ = 1/3 or cosØ = 3/2, the last is not possible
cosØ = 1/3
Ø must be in II or III
Ø = 180  70.529 or Ø = 180 + 70.529
= 109.471° or 250.053°
I assume you know how to change those decimals to degrees and minutes. 
I must respectfully disagree with bob
cos 2T = cos^2 T  sin^2 T = 2cos^2 T  1
bob had it backwards, time for a strong coffee.