HSC Stuff > HSC Mathematics Extension 1

3U Trig

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hanaacdr:
this is the question
i think i wrote it up correctly..


--- Quote from: jakesilove on January 23, 2017, 04:46:50 pm ---For a question like this, I would expand out into just sin(x) and cos(x)







Well, this was a bad idea. I'll leave this here anyway.

Let's break it down into sin(2x)?





Nup. Did you type out the question correctly? If I wolfram alpha the solution, it's pretty damn complicated.

--- End quote ---

kiwiberry:

--- Quote from: hanaacdr on January 23, 2017, 04:01:20 pm ---Hi
i have a similar question,
would i be able to get some help on this,

sin2x + sin3x + sin4x = 0

much appreciated thank you!

--- End quote ---

firstly, sin4x = sin(2*2x)
= 2sin2xcos2x
= 2(2sinxcosx)(2cos2x-1)
= 4sinxcosx(2cos2x-1)

sin3x = 3sinx - 4sin3x

sin2x = 2sinxcosx

let sinx=s and cosx=c

sin2x + sin3x + sin 4x
= 2sc + 3s - 4s3 + 4sc(2c2-1)
= 2sc + 3s - 4s3 + 8sc3 - 4sc
= s(3 - 2c - 4s2 + 8c3)
= s(8c3 - 2c + 4c2 - 1)
= s[2c(4c2-1) + (4c2-1)]
= s(4c2-1)(2c+1)
= s(2c-1)(2c+1)2

not sure if this is right I'm typing on my phone, someone please check!!!

jakesilove:

--- Quote from: kiwiberry on January 23, 2017, 04:55:55 pm ---firstly, sin4x = sin(2*2x)
= 2sin2xcos2x
= 2(2sinxcosx)(2cos2x-1)
= 4sinxcosx(2cos2x-1)

sin3x = 3sinx - 4sin3x

sin2x = 2sinxcosx

let sinx=s and cosx=c

sin2x + sin3x + sin 4x
= 2sc + 3s - 4s3 + 4sc(2c2-1)
= 2sc + 3s - 4s3 + 8sc3 - 4sc
= s(3 - 2c - 4s2 + 8c3)
= s(8c3 - 2c + 4c2 - 1)
= s[2c(4c2-1) + (4c2-1)]
= s(4c2-1)(2c+1)
= s(2c-1)(2c+1)2

not sure if this is right I'm typing on my phone, someone please check!!!

--- End quote ---

That's also what I get to, I just figured it was too complicated!

ellipse:
You could try using sums to products trig identities (turn sin2x+sin4x into 2sin6xcosx). Not really sure if this is 3u stuff though, although it is in the 3u hsc Cambridge book

ellipse:

--- Quote from: ellipse on January 23, 2017, 05:03:54 pm ---You could try using sums to products trig identities (turn sin2x+sin4x into 2sin6xcosx). Not really sure if this is 3u stuff though, although it is in the 3u hsc Cambridge book

--- End quote ---

i meant 2sin3xcosx

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