Question

Find all solutions to the equation in the interval [0,2pi). 2cos^2x+cosx-1=0.
Thanks!

Answer 1

this is a quadratic equation
can you factor it?

Answer 2

Then



It factors



So



or



Hence





or



So



or



Find these values on the unit circle:



bearing in mind that the cosine is represented by the -coordinate of a point on the unit circle and don't miss the fact that your given interval is inclusive of BOTH end points.

Answer 3

please, try this substitution:
\[\cos x=y\]

Answer 4

Refer to the solution process from WolframAlpha.

Answer 5

please substitute y in place of cos x, keep in mind that:
\[(\cos x)^{2}=y ^{2}\]