SOLUTION: Solve the equation in the interval [0,2π] If there is more than one solution write them separated by commas. (cosx)2−1.7cosx−1.68=0

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation in the interval [0,2π] If there is more than one solution write them separated by commas. (cosx)2−1.7cosx−1.68=0      Log On


   

Question 1152781: Solve the equation in the interval [0,2π] If there is more than one solution write them separated by commas.
(cosx)2−1.7cosx−1.68=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%5E2%28x%29-1.7cos%28x%29-1.68=0.....factor
cos%28x%29%5E2%2B0.7cos%28x%29+-+2.4cos%28x%29+-1.68+=+0
%28cos%28x%29%5E2%2B0.7cos%28x%29%29+-+%282.4cos%28x%29+%2B1.68%29+=+0
cos%28x%29%28cos%28x%29%2B0.7%29+-+2.4%282.4cos%28x%29+-0.7%29+=+0
%28cos%28x%29+-+2.4%29+%28cos%28x%29+%2B+0.7%29+=+0

solutions:
cos%28x%29+-+2.4=0=>cos%28x%29=2.4=>x=cos%5E-1%282.4%29=>x=cos%5E-1%282.4%29-> none
cos%28x%29+%2B+0.7+=+0=>cos%28x%29=-0.7=>x=cos%5E-1%28-0.7%29
=>x=2.34619 or x=-2.34619+%2B2pi (result in radians)
=>x=134.4° or x=-134.4%2B360=225.6°

since solution must be in the interval [0,2pi] , =>x=2.34619 radians or x=134.4°