Hey Im totally stuck on this question if somebody could show me a few pointers it would be well appreciated, thank you very much!

Find expressions in sin(nx) and cos(mx) for:

Sin^3(x)

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- November 7th 2012, 10:53 AMKhalif27Trigonometry double angle question
Hey Im totally stuck on this question if somebody could show me a few pointers it would be well appreciated, thank you very much!

Find expressions in sin(nx) and cos(mx) for:

Sin^3(x) - November 8th 2012, 02:13 PMStefanTMRe: Trigonometry double angle question
Hi Khalif27,

you have to apply (a+b)^3=a^3+3*a^2*b+3a*b^2+b^3

and i^2=-1, i^3=-i,

from the formula Moivre's you have:

(cosx+isinx)^3=(cos3x+isin3x)

(cosx+isinx)^3= cos^3(x)+3icos^2(x)*sin(x)-3cos(x)*sin^2(x) -icox^3(x)

= cos^3(x)-3cos(x)*sin^2(x) + i*[3cos^2(x)*sin(x)-sin^3(x)]

==> cos(3x)= cos^3(x)-3cos(x)*sin^2(x) = cos^3(x)-3cos(x)*(1-cos^2(x))=4cos^3(x)-3cos(x)

and sin(3x)= 3cos^2(x)*sin(x)-sin^3(x) =3(1-sin^2)*sin(x)-sin^3(x)=3sin(x)-4sin^3(x)