Question

Factor the algebraic expression below in terms of a single trigonometric function.

cos x - sin ^2x - 1

Answer 1

you remember the property from the unit circle.
\[\large \sin^2(x)+\cos^2(x) = 1\]

Answer 2

Yes I do

Answer 3

Solve that for sin^2(x)
\[\sin^2(x)=1-\cos^2(x)\]

Put that sin^2(x) into the expression for sin^2(x)

\[\cos(x)-(1-\cos^2(x)) -1\]

Answer 4

That gives you
\[\large \cos^2(x) + \cos(x) - 2\]

Answer 5

You can factor that out to
\[\large (\cos x + 2)*(\cos x - 1)\]

Answer 6

Oh wow okay thanks!