General solution question (1 Viewer)

[Grey Council]

Find general solution to the following equation:
sin3x = sin2x

:-\

 

[George W. Bush]

Straight forward general solution application with (-1)^n 3x or (-1)^n 2x

then make x the subject...

 

[NiKz*~]

i dun get it..=/
how do u do it?

 

[Grey Council]

hoy, Bush. Can you post up a full solution? I don't get it either. :-\

 

[Xayma]

Well sin3x=sin2x when both sides =0 ie x=0/pi/etc
There is another solution but Ill post the working up in a second.

sin 3x=sin 2x
sin 2x cos x+cos 2x sin x=2sin x cos x
3sin x cos² x -sin ³ x=2sin x cos x
3cos² x -sin² x=2cos x
4cos² x -1=2cos x

Let u=cos x
:. 4u²-2u-1=0

solving we get u=[1+sqrt(5)]/4

Doing the inverse cos we get x=pi/5 or 3pi/5.

Therefore the general solution is x= pi/5+n(pi) or x=3pi/5 +n(pi) or x= n(pi)

 

[Affinity]

or you can do:

sin(3x) - sin(2x) = 0

sin(2.5x + 0.5x) - sin( 2.5x - 0.5x) = 0

simplifies to:

2cos(2.5x)sin(0.5x) = 0

and you can work the rest out I hope

 

[CM_Tutor]

Extn 2 students - note Affinity's approach. You should be able to use the sums-to-products formulae.

 

[DcM]

this is from fitzp. 3u book

mm..that answer says its 2n(pi) or (4/5)n +_ (pi)/5

 

[DcM]

ohhh i fink i get it now

its outta the syllabus..from 3 u anyway cos u use affinity's method

 

[Xayma]

Originally posted by Affinity
sin(2.5x + 0.5x) - sin( 2.5x - 0.5x) = 0

Hmm alot simpler *notes that down. Damn tendency to work in whole units.

 

[George W. Bush]

sin3x=sin2x

3x = (pi)n + (-1)^n 2x, where n= etc.

Making x the subject

x = n(pi)/[3 - 2(-1)^n]

If you use 2x = ...., you'll get the same thing range of answers, except you'll need different n values for them