Trig
posted by Waldo .
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.
Respond to this Question
Similar Questions

PreCalculuscheck answers
If cos theta = 0.8 and 270<theta<360, find the exact value of sin 2theta a) 0.96 b) 0.6 c) 0.96 d) 0.28 Answer: b 2) If csc theta = 5/3, and theta has its terminal side in Quadrant III, find the exact value of tan 2theta a)24/25 … 
Trig
Given 2secant^2 (theta) + 1 = 5 secant (theta), solve for (theta), to the nearest degree, in the interval 0 degrees is greater than or equal to (theta) which is less than 360 degrees 
trig
Find all values of [theta] in the interval 0°<=X<= 360° that satisfy the equation cos2[theta]cos[theta]=0 
trig
what are the values of theta in the interval 0 degrees is lessthan or equal to theta is less than or equal to 360 degrees that satisfy the equation tan theta minus square root of 3 equals 0? 
trig
find two values of theta, zero degrees is than or equal to theta which is less than 360 degrees, that satisfy the given trigonometric equation. tan theta equals radical 3. 
Trigonometry
find all values of theta in the interval 0<theta<360 that satisfy the equation 3cos 2theta + 2 sin theta+1=0 
trig
i nead to find to the nearest degree all values of theta in the interval 0 x 360 that satisfy the equation 3 cos 2 theta+ sin theta1=0 
Math Trig Please Help!!!
Find exact values for all the solutions to the equation cos theta = sqrt 3/2 for 2pi <= theta <= 2pi Theta = Theta = Theta = Theta = 
Calculus Question! ASAP!
Hello! I have this problem: x(dx)/sqrt(9x^2) I was wondering why I can't use trig substitution and substitute sqrt(9x^2) for sqrt(1sec^2) and having: integral x = 3sin(theta) dx = 3cos(theta)d(theata) integral 3sin(theta)(3cos(theta))/3cos(theta) … 
Math trigonometry
8sin^2theta+10 sin theta cos theta =3cos^2 theta=0 then general solution for theta is