Question

Solve sin(9x) + sin(7x) for all values of x

Answer 1

You can't solve something if it's not an equation...

Answer 2

what to solve sin(9x)+sin(7x)=0?

Answer 3

\(\sin(9x) + \sin(7x)\) is just simply \(\sin(9x) + \sin(7x)\)

Answer 4

It should be sin(9x) + sin(7x) = 0

Answer 5

\[\sin(p+q)=\sin(p)\cos(q)+\cos(p)\sin(q)\]\[\sin(p-q)=\sin(p)\cos(q)-\cos(p)\sin(q)\]\[\sin(p+q)+\sin(p-q)=2\sin(p)\cos(q)\]\[p+q=9x\]\[p-q=7x\]
\[p=8x\]\[q=x\]Then the equation:\[\sin(9x)+\sin(7x)=2\sin(8x)\cos(x)=0\]
You only need to find the x´s that make \[\sin(8x)=0\rightarrow x=k\frac{ \pi }{ 8 }\] or\[\cos(x)=0\rightarrow x=(2k-1)\frac{ \pi }{ 2 }\]
where k=0,1,2.....

Answer 6

The idea is that whenever you have an equation built with sin and cos, the best thing is to convert it into a product

Answer 7

Good answer, but does it find all solutions? http://www.wolframalpha.com/input/?i=sin%289x%29+%2B+sin%287x%29+%3D+0

Answer 8

Compared to http://www.wolframalpha.com/input/?i=2sin%288x%29cos%28x%29%3D0

Answer 9

Seems odd that wolfram even shows an equivalent form of it as sin(9x)+sin(7x) in the second link...

Answer 10

agent0smith You are right, I should have said: k=0, +/-1, +/-2,...
(must be my positive thinking...:)

Answer 11

Still, it's odd that wolfram displays the solutions so differently for two equivalent functions... and look at the number line at the bottom of each link, the solution sets are not the same (the original form has far more solutions than the modified form).

Answer 12

well the solutions given by Wolfram for cos(x)=0 is \[x=\pi n-\frac{ \pi }{ 2 }=(2n-1)\frac{ \pi }{ 2 }\]which is the same as mine. I will analyze the first link because it seems quite an obscure method

Answer 13

Yeah I know your solution is the same as the second link. It's the first that seems odd.

Answer 14

unnecessarily complicated I would say (which proves there is a machine behind...)

Answer 15

http://www3.wolframalpha.com/Calculate/MSP/MSP14421f4ehfebdi5fac500000164e95117258gcf7?MSPStoreType=image/gif&s=23&w=310.&h=36.

http://www3.wolframalpha.com/Calculate/MSP/MSP4055208efh6e81g1h12b00000h34eb6f1ad76gfc?MSPStoreType=image/gif&s=30&w=310.&h=36.

But these aren't the same solution sets...

Answer 16

I think maybe it just doesn't show them all in the second :/

Answer 17

First time I see Wolfram. Fishy thing, solutions are supposed to be periodic and this is not what they look like in second link

Answer 18

Yeah, the graphs look exactly the same...

http://www.wolframalpha.com/input/?i=y%3D+sin%289x%29+%2B+sin%287x%29++from+x%3D-20+to+20

http://www.wolframalpha.com/input/?i=y%3D+2sin%288x%29cos%28x%29+from+x%3D-20+to+20

So i think it was some kinda mistake.