3 Unit Maths (1 Viewer)

[Csteele]

Hello Everyone!
Been reading these forums for a while, but my first post!
Anyway....

I missed a few days of school while my class was doing 'Sums and differences of Angles'. Been doing it today and ive got the hang of it just a few questions i cant get which i would LOVE help with.

1. By writing 3x as 2x+1x, find an expression in the terms of 'x' for

a) Sin 3x
b) Cos 3x
C) Tan 3x

Your help would be much apreciated.

Cam.

 

[watatank]

tan(a+/-b) = (tana +/- tanb)/(1 -/+ tana.tanb)

sin(a +/- b) = sina.cosb +/- cosa.sinb

cos(a +/- b) = cosa.cosb -/+ sina.sinb

those are the formulas you need. good luck.

 

[Csteele]

Thanks. But i know the formulas. But you sub them in and i just dont know where to go from there.

Answers (according to back of book)

a) 3sinx cos^2x - sin^3x
b) cos^3x - 3 sin^2x cosx
c) (3tanx - tan^3x)/(1 - 3 tan^2x)

Now i really have no idea how they got these answers. Any help?

 

[tommykins]

sin(2x+x) = sin2xcosx + cos2xsinx.

Change the 2x's to x+x.

sin(x+x)cosx + cos(x+x)sinx.

Expand .

(sinxcosx + sinxcosx)cosx + (cos^2x - sin^2x)sinx.

= 2sinxcos^2x + cos^2xssinx - sin^3x.

Convert all cos^2x to 1-sin^x. collect terms, factorise and

voila!

same goes for all others.

 

[Zephyrio]

Well...

a) sin 3x = sin (2x + x)
= sin2x.cosx+sinx.cos2x
= 2cosxsinx.cosx + sinx.(cos^ x-sin^2 x)
= 2cos^2 sinx + sinxcos^2 x - sin^3 x
= 3sinxcos^2 x - sin^3x.

b) cos 3x = cos (2x + x)
= cos2x.cosx - sin2x.sinx
= (cos^2x-sin^2x)cosx - 2cosxsin^2x
= cos^3x - sin^2xcosx - 2cosxsin^2x
= cos^3x - 3cosx.sin^2x

c) tan 3x = tan (2x + x)
then follow in the same vain and you'll get it. Convert the tan 2x to (tan2x-tanx)/(1-tan2x.tanx). I don't want to do it because there are fractions and it's such a pain to type up math onto the comp. But if you're stuck we can help more =P

Hope that helps. You are basically converting the cos 2x, sin 2x and tan 2x.

 

[Csteele]

Got it! Thanks mate.