SOLUTION: Solve cos2&#952; + cos&#952; = 0 for 0° &#8804; &#952; < 90°.

Algebra ->  Trigonometry-basics -> SOLUTION: Solve cos2&#952; + cos&#952; = 0 for 0° &#8804; &#952; < 90°.      Log On


   

Question 861386: Solve cos2θ + cosθ = 0 for 0° ≤ θ < 90°.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
cos%282%2Atheta%29%2Bcos%28theta%29=0
cos%5E2%28theta%29-sin%5E2%28theta%29%2Bcos%28theta%29=0
cos%5E2%28theta%29-sin%5E2%28theta%29%2Bcos%28theta%29=0
cos%5E2%28theta%29-%281-cos%5E2%28theta%29%29%2Bcos%28theta%29=0
cos%5E2%28theta%29-1%2Bcos%5E2%28theta%29%2Bcos%28theta%29=0
2cos%5E2%28theta%29%2Bcos%28theta%29-1=0
Let u=cos%28theta%29
2u%5E2%2Bu-1=0
%28u%2B1%29%282u-1%29=0
Two solutions:
u%2B1=0
u=-1
cos%28theta%29=-1
theta=pi
Not in the solution region.
2u-1=0
2u=1
u=1%2F2
cos%28theta%29=1%2F2
theta=pi%2F3 and theta=%285%2F3%29pi
Only theta=pi%2F3 is in the solution region.
theta=pi%2F3=60degrees