Question

Solve the following for θ, where θ is greater than or equal to 0 and less than 2π: 2cos^2θ-5cosθ=3

I factored it out to (cos^2θ-3)(2cos^2θ+1)=0 but got answers of cosθ=(√3) and cosθ=(√-1/2) which doesn't make sense so I think i'm doing it all wrong.

Answer 1

well your factorisation is slightly wrong

try

\[(\cos(\theta) -3)(2\cos(\theta) + 1) = 0\]

so the solutions are

\[\cos(\theta) = 3, \frac{-1}{2}\]

the\[\cos(\theta) = 3\] solution

doesn't exist so ignore it as a solution just find the values where

\[\cos(\theta) = \frac{-1}{2}\]

in the given domian

Answer 2

Ahh thank you, that makes much more sense! I got 2π/3 and 4π/3 :)

Answer 3

yep... thats it..