Trigonometry Identity problem I been trying to solve all day

[Juliano]

Homework Statement

solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2pi

Homework Equations

The Attempt at a Solution

3(cos(x) + 1) = 2 sin^2(x)
3(cos(x) + 1) = 2 (1- cos^2(x))
I've tried this variation, and a couple others but it just does not pan out. Please help.

Oh yeah we have a real uninformative book.

 

[yeongil]

3(cos(x) + 1) = 2 sin^2(x)
3(cos(x) + 1) = 2 (1- cos^2(x))
I've tried this variation, and a couple others but it just does not pan out. Please help.

Oh yeah we have a real uninformative book.

Don't factor out the 3 on the left side. Instead, distribute the right side, and move everything to the left side. After doing that, do you recognize the equation?


01

 

[Juliano]

OK so I get the following
3 cos(x) + 3 = 2 - 2 cos^2(x)
3 cos(x) + 1 + 2 cos^2(x)=0
I tried this variation before, but I was unsure of what to do with the 1+2 cos^2(x) part. or maybe I'm just doing something wrong with the distribution and movement of the right side.

 

[Juliano]

hold on I think I understand now.
(3 cos(x)+1)(2cos^2(x))= 0, the solve those two for 0

 

[yeongil]

No no no, that's not right. It's best if you put the equation in "standard form" first, like this:
2cos^2(x) + 3 cos(x) + 1 = 0
Do you see what to do now?


01

 

[Juliano]

wow. My head was so wrapped up in Identities I didn't even think to factor them in standard form
(cos +1)(2cos+1)=0
Thank you for shining a light through this fogged up brain of mine

 

[Mark44]

hold on I think I understand now.
(3 cos(x)+1)(2cos^2(x))= 0, the solve those two for 0

Althought the correct approach has already been pointed out, the equation above deserves a further comment. You can't get to the equation above from the one you showed in a previous post:

3 cos(x) + 1 + 2 cos^2(x)=0

If you multiply out your factored form, you get only two terms, not the three shown just above.

 

[Juliano]

Yeah I see what you mean Mark44, Teachers always tell you to double check doing what you just did. Maybe I need to start doing that more.

 

[Mark44]

Yeah, maybe you should, especially when you're in the early stages of learning something.