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.
u= 1/3 u= -2/3
so what angles are those?
3(2cos^2 Ø - 1) = 7cosØ
6cos^ Ø - 7cosØ - 3 = 0
(3cosØ+1)(2cosØ-3) = 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.