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Jamierox4ev3r
 one year ago
Find all values of x such that sin 2x = sin x and ________________.(List the answers in increasing order.)
Jamierox4ev3r
 one year ago
Find all values of x such that sin 2x = sin x and ________________.(List the answers in increasing order.)

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Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1wow, hold on, a certain part of the question isn't coming out right...

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1"Find all values of x such that sin2x=sinx and \(0\le x \le 2\pi\). (List the answers in increasing order)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3there are at least two ways to solve this il show you the first/fast way quick

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\sin(2x) = \sin (x)\) since \(\sin(t)\) has a period of \(2\pi\), we must have \[2x=x+2n\pi \implies x = 2n\pi\tag{1}\] since \(\sin(t)=\sin(\pit)\), we must have \[2x=\pix+2n\pi\implies x =\dfrac{\pi}{3}+\dfrac{2n\pi}{3} \tag{2}\] plugin \(n=0,1,2\ldots\) and take the solutions that are within the given interval

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3if you don't like that method, try using below identity : \[\sin(2x) = 2\sin x\cos x\]

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1oh right! that's one of the double angle identities, if I'm not mistaken

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes put everything on one side and try factoring

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\sin 2x = \sin x\) \(2\sin x\cos x = \sin x\) \(\sin x(2\cos x1) = 0\) use ur favorite zero product property

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1put everything on one side? So do you mean set this equation to zero?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3yes, i did t that already for you

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1yep, that's what you meant. and oooh yeah you mentioned this before. My favorite indeed/

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1hmmm.... so upon solving, I see that we can have \(\Large 0, \frac{\pi}{3}, \pi , \frac{5\pi}{3}\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1Am i missing any?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you're missing just one

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1oh, would that be \(2\pi\)?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes, \(x=2\pi\) satisfies \(\sin(x)=0\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1I forgot that in this scenario, it wasn't excluded. Well alright, I think I got it.

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.1Thank you! You're terrific at explaining things \(\ddot\smile\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3np im as terrific as you're smart at picking up on these :)
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