Posted by **Greg** on Wednesday, November 14, 2012 at 3:12pm.

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

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

- Trigonometry -
**Reiny**, Wednesday, November 14, 2012 at 3:50pm
cos^2 Ų - cosŲ - 6 = 0

let cosŲ = x , then we get

x^2 - x - 6 = 0

(x-3)(x+2) = 0

x = 3 or x = -2

then cosŲ = 3 or cosŲ = -2

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

there is no solution to your equation

- Trigonometry -
**Steve**, Wednesday, November 14, 2012 at 4:43pm
also, you coul dhave reasoned thus:

cos^2θ <= 1

-1 <= cosθ <= 1

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

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