SOLUTION: 10cos^2x+9cosx+2=0 find all solution in the interval [0,360)? the answer is 113.58,246.42,120,240 i needed step by step solution

Algebra ->  Trigonometry-basics -> SOLUTION: 10cos^2x+9cosx+2=0 find all solution in the interval [0,360)? the answer is 113.58,246.42,120,240 i needed step by step solution      Log On


   

Question 1053554: 10cos^2x+9cosx+2=0 find all solution in the interval [0,360)?
the answer is 113.58,246.42,120,240
i needed step by step solution
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=cos%28theta%29
10u%5E2%2B9u%2B2=0
Now just solve it like a quadratic equation,
Factoring,
%285u%2B2%29%282u%2B1%29=0
So then,
5u%2B2=0
5u=-2
u=-2%2F5
cos%28theta%29=-2%2F5
Use a calculator to solve for the two values.
and,
2u%2B1=0
2u=-1
u=-1%2F2
cos%28theta%29=-1%2F2
Again use a calculator or from your previous studies,
theta=120 and theta=240