## anonymous 3 years ago Solve the equation: a.) 2 cos^2x-cos x=1

1. anonymous

let's define $t:= \cos(x)$ we have the quadratic equation: $2t^2-t=1$ can you find it's solutions?

2. anonymous

Would it be cos=1? Which means cos=0 degrees or 360 degrees?

3. anonymous

there are two solutions, $\cos(x)=1$ and $\cos(x)=-\frac{1}{2}$ so x can be either $360^\circ{} k$ (for every integer k) or $120^\circ{}+ 360^{\circ}k$ or $240^\circ{}+ 360^{\circ}k$