SOLUTION: Use trigonometric identities to solve cos(2&#952;)+cos(&#952;)=0 exactly for 0&#8728;&#8804;&#952;<360&#8728;. If there is more than one answer, enter your answers as a comma separ

Algebra ->  Trigonometry-basics -> SOLUTION: Use trigonometric identities to solve cos(2&#952;)+cos(&#952;)=0 exactly for 0&#8728;&#8804;&#952;<360&#8728;. If there is more than one answer, enter your answers as a comma separ      Log On


   

Question 869656: Use trigonometric identities to solve cos(2θ)+cos(θ)=0 exactly for 0∘≤θ<360∘. If there is more than one answer, enter your answers as a comma separated list.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

So,
cos%282theta%29%2Bcos%28theta%29=0 can be re-written as
2%28cos%28theta%29%29%5E2%2Bcos%28theta%29-1=0
and if we abbreviate it by defining y=cos%28theta%29
we can re-write it as
2y%5E2%2By-1=0
That quadratic equation can be solve by factoring,
or by completing the square,
or by using the quadratic formula,
to yield the solutions
system%28y=-1%2C%22or%22%2Cy=1%2F2%29 .
Going back to theta and for 0%5Eo%3C=theta%3C360%5Eo
we find that y=cos%28theta%29=-1 ---> highlight%28theta=180%5Eo%29
and y=cos%28theta%29=1%2F2 ---> system%28highlight%28theta=60%5Eo%29%2C%22or%22%2Chighlight%28theta=300%5Eo%29%29