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satellite73
 4 years ago
i have a question. why is the solution to
\[sin(3x)=\sin(2x)\]
\[x=\frac{\pi}{5}, x=\frac{3\pi}{5}\]?
satellite73
 4 years ago
i have a question. why is the solution to \[sin(3x)=\sin(2x)\] \[x=\frac{\pi}{5}, x=\frac{3\pi}{5}\]?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i mean i worked it out and found this answer, but the last step of my solution required finding \[\cos^{1}\left (\frac{1\sqrt{5}}{4}\right)\] so i am wondering if there is a snappy way to do it, because the answer is so neat and clean.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0my answer is here http://openstudy.com/study#/updates/4f23fcc4e4b0a2a9c26655ef

phi
 4 years ago
Best ResponseYou've already chosen the best response.1@sat my instinct was to take your approach. But looking further, I see sin(a)  sin(b)= 2 cos(0.5(a+b)) sin(0.5(ab)) gets us to the answer in a snappy way

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@phi, wow it sure does, doesn't it!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0for \[\cos x = \frac{1+ \sqrt5}{4}\] and \[\cos x = \frac{1 \sqrt5}{4}\] Since x=pi/5 is a solution to \[\cos x = \frac{1+ \sqrt5}{4}\] x=pi/5+2kpi are also solutions (k is an integer) also, x=pi/5+2kpi are also solutions. since cos(x)=cos(x) Similarly since x=3pi/5 is a solution to \[\cos x = \frac{1 \sqrt5}{4}\] x=3pi/5+2kpi are also solutions (k is an integer) also, x=3pi/5+2kpi are also solutions. since cos(x)=cos(x) And for sin (x) = 0 we have x = 0 + kpi are solutions. Therefore, the solutions to the equation sin(2x)=sin(3x) are \[x = k \pi\] \[x=2k \pi \pm \frac{\pi}{5}\] and \[x=2k \pi \pm \frac{3\pi}{5}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm only continuing on satellite73's response in the attached link.

phi
 4 years ago
Best ResponseYou've already chosen the best response.1@tomas: replace sin^2(x) with 1cos^2 x you get sat's equation

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327764356757:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it means 2n\[2n \Pi + 1^{n} \times b\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0phi's answer is short and sweet and makes it clear, but i am still wondering why, when you take \[\cos^{1}\left(\frac{1\sqrt{5}}{4}\right)=\frac{\pi}{5}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i mean other than the fact that it is true. why is \[\cos(\frac{\pi}{5})\] the same as the solution to \[4x^22x1=0\]
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