Use factoring, the quadratic formula, or identities to solve the equation. Find all solutions in the interval [0, 2π). (Round each answer to three decimal places.)

cos(2x) + sin(x) = 1

Question

Use factoring, the quadratic formula, or identities to solve the equation. Find all solutions in the interval [0, 2π). (Round each answer to three decimal places.)

cos(2x) + sin(x) = 1

anonymous · Answer

Do you recall the double angle cosine identity?

anonymous · Answer

Anything?

anonymous · Answer

Sorry, I was getting help for my homework.

I believe I remember it.

cos(2x)=1-sinx or something along those lines?

anonymous · Answer

I guess I should just plug and play from there if that is right...

anonymous · Answer

$$\cos(2x) = 1 - 2\sin^2(x)$$
This one is nice because it puts x in terms of only sin.

anonymous · Answer

So just plug in the identity there in the equation given..

anonymous · Answer

It works out nicely. You should get 4 solutions on the interval.

anonymous · Answer

Workin' it out now.  Looks a little crazy at first, so I'm trying to figure it out.

anonymous · Answer

You should end up with factors of sin(x)

anonymous · Answer

Awesome, thanks for the tip.

anonymous · Answer

No problem. Let us know what you came up with.

anonymous · Answer

It was an between interval [0, 2π):

0, π/6, 5π/6, π

anonymous · Answer

Got it right on the assignment, too.  So, thanks again!

anonymous · Answer

Perfecto.