A university maths question.... (1 Viewer)

[BlackJack]

I don't get this particular q...

(given, from previous parts.)
c=1+cos@.cos@+cos^2@.cos2@+...cos^(n-1)@.cos(n-1)@
s=cos@.sin@+cos^2@.sin2@+...cos^(n-1)@.sin(n-1)@

c+is=(1-cos^n@.e^[in@])/(1-cos@.e^[i@])

(1-cos@.e^[i@])(1-cos@.e^-1@)=sin^2@

Hence, show
c=1+(cos^n@.sin(n-1)@)/sin@
and find a similar expression for s.

I'm trying to find a way to express the real part of c + is after I slot the fourth equation into the third, but I can't rearrange the third one to suit it.

Any hints? It's for an assignment, so no full answers right now plz.

(hmmm... btw, e^[i@]==cos@ + isin@... and e^[-i@]==cos@ - isin@)

 

[spice girl]

Hint?

I think this might be useful:

sin(n-1)@sin@ = cos(n-1)@cos@ - cosn@

 

[BlackJack]

"What? Impossible!!!! How can I have not seen this before?!?!"
lol, thanks alot.

 

[McLake]

BJ, take your uni maths out of here.

 

[bobo123]

just looking at that makes me scared of uni


i heard from me teacher using eulers would make complex numbers in school easy
i still have no idea what his on about

 

[SoFTuaRiaL]

Originally posted by bobo123


i heard from me teacher using eulers would make complex numbers in school easy
i still have no idea what his on about

euler's formula says that (cos@ + isin@) can be written as e^(i@)
associated with it are various properties n stuff .... ur teacher's right, it does make it easier, but its not a part of the HSC syllabus. infact, euler's formula makes integration of sines n cosines so much more easier ...

 

[routemarker]

ha at High school cos@ + isin@ = cis@ = e^i@
my lecturer totally baged out sis notation as it is only found in NSWlol and ppl outside of NSW would probably have never heard of it and it is not in any respectable text.

 

[KeypadSDM]

Cis[@] notation isn't even recognised in NSW HSC syllabuses, none of the 4.

Although it does make it a hell of alot easier to write...