Question

find the general solution for sinx=1-2cos^2x. I have already found that x=7pi/6, 11pi/6 and pi/2; I just need help finding the general solution.

I can never understand how to find the general solution ;_;

thankss!! (last question i promise lol)

Answer 1

@ganeshie8 wanna help me again :x or anyone really

Answer 2

\[\Large\begin{array}{rcl}
\sin x&=&1-2\cos^2x\\
\sin x&=&1-2(1-\sin^2x)\\
\sin x&=&1-2+2\sin^2x\\
2\sin^2x-\sin x-1&=&0\\
(2\sin x+1)(\sin x-1)&=&0\\
2\sin x+1=0&\text{or}&\sin x-1=0\\
\sin x=-0.5&\text{or}&\sin x=1\\
x=\frac{11\pi+2m\pi}6\text{ or }x=\frac{7\pi+2n\pi}6&\text{or}&x=\frac{\pi+2p\pi}2
\end{array}\]

Answer 3

@ganeshie8 lolz u faster :P

Answer 4

thanks @kc_kennylau, but can you explain the method in which you arrived at the general solution? and what is the difference between the m and n?

Answer 5

just giving 'em different names :)

Answer 6

wait sorry it should be:
\[\Large x=\frac{7\pi}6+2m\pi\text{ or }x=\frac{11\pi}6+2n\pi\text{ or }x=\frac\pi2+2p\pi\]

Answer 7

because \(\sin\)'s period is \(2\pi\) :)

Answer 8

ohh so its as easy as adding 2pi? because I knew that rule but I didn't know if I could apply it here. btw how do you type it in the cool equation form thing in different lines? I try doing that but it only allows me to enter one continuous line?

Answer 9

do you know how to type latex instead of just clicking the equation button? :)

Answer 10

like really typing out the code

Answer 11

nope. oh well. thanks for the help anyways!