Question

2cos^2theta=2+sin theta
Please help me! Thank you so much, this is really appreciated, I'm having difficulty with these examples. :)

Answer 1

\[\cos^2(\theta) = 1 - \sin^2(\theta)\]

Answer 2

substitute that and solve like a quadratic

Answer 3

Hello, Avi,

Weren't there instructions with \[2(\cos^2\theta)=2+\sin \theta\] ?

Please provide as much info as you can about what you want to accomplish.

I can guess (but wish I didn't have to): You are to solve the given equation for theta:

There is a very useful identity for (cos theta)^2. Mind doing some review, to find it?
Get rid of the (cos theta)^2 and replace it with its equivalent.

Answer 4

okay, thanks! I couldn't find my formula sheet, it didn't click at first that that was what I ought to do.

Answer 5

and it was just shown as the problem, that was all the info I had, sorry.

Answer 6

so,
\[2(1-\sin^2(\theta)) = 2 + \sin(\theta)\]\[2 - 2\sin^2(\theta) = 2 + \sin(\theta)\]\[-2\sin^2(\theta)-\sin(\theta)=0\]\[(\sin(\theta))(-2\sin(\theta)-1)=0\]

so
\[\sin(\theta) = 0\]or\[\sin(\theta)=-1/2\]

Answer 7

Thanks! The step by step was very informative!

Answer 8

No Problem