Question

how can i solve sin(7x)=sin(5x)????
is it correct to do
sin(5x+2x)=sin(5x)??

Answer 1

how do you get rid of a "sin" function i an equation?

Answer 2

in*

Answer 3

.... sin^-1....???

Answer 4

so do that to both sides of the equation and see what you get

Answer 5

x=0?

Answer 6

after you get rid of the "sin" in the equation 'sin(7x)=sin(5x)', what are you left with?

Answer 7

7x=5x??

Answer 8

whats the only number that makes that true?

Answer 9

You can't get rid of a sin function in an equation btapia... It's a function.

Answer 10

oh man... this is hard...........

Answer 11

0 works... Are you in Precalc?

Answer 12

yea the only number that makes '7x=5x' true is 0
true? or no?

Answer 13

but the graph shows a lot of intersection......

Answer 14

No, Do you have an interval over which to solve this?

Answer 15

-2pi to 2pi

Answer 16

Don't listen to btapia he has no idea what he is talking about.

Answer 17

but i have to do it algebraically.....

Answer 18

how did u get from sin7x=sin5x to 5x+2pi(k)=7x??? wat did u do??

Answer 19

You know the period is 2pi right?

Answer 20

Sorry I didn't mean to delete that last comment...

Answer 21

so u just get rid of the sin and add 2kpi in it.......??

Answer 22

You take the sin(5x)=sin(7x) and add the period of sin(5x), which is 2pi(k) which is 5x+2pi(k) and set it equal to the sin(7x) giving you 5x+2pi(k)=7x
2x=2pi(k)
x=pi(k)
So it intersects every pi(k).

Answer 23

So at -2pi, pi, 0, pi, 2pi

Answer 24

Here's one way. It relies on a trick, and there might be a nicer way, but here goes.
sin(7x)-sin(5x)= 0

rewrite 7x as 6x+x, and 5x as 6x-x

sin(6x+x)- sin(6x-x)=0
expand the sin(6x+x) = sin(6x)cos(x)+cos(6x)sin(x)
expand -sin(6x-x)= -sin(6x)cos(x)+cos(6x)sin(x)

add the 2 equations to get
2cos(6x)sin(x)=0
or
cos(6x)sin(x)=0

now find all the x values in your interval that make either cos(6x)=0 or sin(x)=0

Answer 25

oh wow i get it now~~~ thank you~~

Answer 26

phi's way works too, but seriously don't listen to btapia...

Answer 27

yeah~~ i can sleep now~~~ XDDD