Question

Express sin 3x in terms of sin x.
PLEASE HELP!

Answer 1

lol dat user name.

So it's \(\Large\rm \sin3x\), yes?
Not to be confused with \(\Large\rm \sin^3x\)

Answer 2

yes its sin 3x

Answer 3

my username OP

Answer 4

I've only played a few games with Riven, still trying to get the hang of her >.<
I main Elise in Jungle.

Answer 5

So I guess we need to make use of our Angle Identity Formula for Sine.

Answer 6

Angle Addition I meant to say*

Answer 7

lol honorary professor of mathematics plays league

Answer 8

\[\Large\rm \sin(3x)=\sin(2x+x)\]

Answer 9

\[\Large\rm \sin(a+b)=\sin a \cos b +\sin b \cos a\]

Answer 10

Understand how we can use this formula to start breaking things down?

Answer 11

yeah i know this i just didnt know i forgot to apply it

Answer 12

so that would be sin2xcosx+sinxcos2x

Answer 13

Ok great. First step is done.

Answer 14

From there to deal with the 2x angles, we'll apply our `Double Angle` Identities.

Answer 15

\[\Large\rm \sin(2x)=2\sin x \cos x,\qquad\qquad \cos(2x)=1-2\sin^2x\]

Answer 16

so that would be \[2 \sin x \cos ^{2}x +\sin x \left( 1-2\sin ^{2} x\right)\]

Answer 17

@zepdrix

Answer 18

Mmm ok.
So now we have a cos^2x to deal with.
Remember your Pythagorean Identity for sine and cosine?

Answer 19

yes

Answer 20

\[\Large\rm \sin^2x+\cos^2x=1\qquad\to\qquad \cos^2x=1-\sin^2x\]

Answer 21

so you plug that in

Answer 22

\[\Large\rm 2\sin x \left(1-\sin^2x\right) +\sin x \left( 1-2\sin ^{2} x\right)\]Yes.
And it shouldn't be to bad after that.
Just need to distribute some stuff... and combine like terms.

Answer 23

so that gives you\[3\sin x -4\sin ^{3}x\]

Answer 24

Yay good job!

Answer 25

is that the final answer?

Answer 26

Yes.

Answer 27

It's now it terms of sin(x), only x as the angle.

Answer 28

YES THANK YOU THANK YOU THANK YOU

Answer 29

lol np :3