What value(s) of theta solve the following equation? cos^2(theta)-cos(theta)-6=0?

Question

I try plugging in different numbers but I am not sure exactly what I am looking for in order to solve?

Answer 1

cos^2 Ø - cosØ - 6 = 0

let cosØ = x , then we get

x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3 or x = -2
then cosØ = 3 or cosØ = -2

both of these are not possible, since the cosine is defined only between -1 and +1

there is no solution to your equation

Answer 2

also, you coul dhave reasoned thus:

cos^2θ <= 1
-1 <= cosθ <= 1

no way could you have cos^2θ - cosθ = 6