Question

Can anyone help me with finding cos 3x?

Answer 1

I understand that cos(A+B) = cosAcosB - sinAsinB

So I got

cos3

cos(2x+1)

cos2xcosx-sin2xsinx

(2cos^2-1)cosx -2sincosx?

How do people get to the part of switching the sinx to cos????
Please help, thanks.!

Answer 2

cos(x+x) = cos^2 (x) sin^2(x)
sin(x+x) = 2 sin(x) cos(x)

Answer 3

cos(2x) cos(x) - sin(2x) sin(x)

(cos^2(x) - sin^2(x)) cos(x) - 2 sin(x) cos(x) sin(x)

Answer 4

But how did you go from the sin part of -sin2xsin into -2sincos

I understand that sin2x=2sinxcos, but what happened to the sin in -sin2xsin

should it be 2sinxcox(sinx)?

Answer 5

what is the identity for: sin(x+x)

Answer 6

oh, you wrote it ...

Answer 7

since the last part there is\[-sin(2t)~sin(t)\]
and sin(2t) = 2sin(t)cos(t), replace it
\[-[sin(2t)]~sin(t)\]
\[-[2~sin(t)~cos(t)]~sin(t)\]
\[-2~sin(t)~cos(t)~sin(t)\]

Answer 8

forgot it was an x, not a t

Answer 9

(2cos^2-1)cosx -2sin^2cosx

2cosx^3-cosx-2sinx^2cosx. Is this correcg?

Answer 10

hmmm, id have to collect terms and whatnot

(cos^2(x) - sin^2(x)) cos(x) - 2 sin(x) cos(x) sin(x)

cos^3(x) - sin^2(x)cos(x) - 2 sin^2(x) cos(x)

cos^3(x) - (1-cos^2(x))cos(x) - 2 sin^2(x) cos(x)

cos^3 - cos+ cos^3 - 2 sin^2 cos

2cos^3 - cos (1 - 2 sin^2)

there are prolly a few different ways to restructure it

Answer 11

sin^2 = 1-cos^2

2cos^3 - cos (1 - 2 (1-cos^2))

2cos^3 - cos (1 - 2 + 2 cos^2)

2cos^3 - cos ( - 1 + 2 cos^2)

2cos^3 + cos + 2 cos^3

4cos^3 + cos

Answer 12

prolly got some errors in there

Answer 13

\[cos(3 x) = cos^3(x)-3 sin^2(x) cos(x)\]

Answer 14

in the end after i fix my few erros :)
\[cos(3 x) = 4 cos^3(x)-3 cos(x)\]

Answer 15

wait, i have to do more.

2cos^3-cosx-2(1-cosx^2)cosx

2cos^3-cosx-2cosx+2cos^

4cos^3-3cosx

Answer 16

Thanks for helping.

Answer 17

youre welcome

Answer 18

Wait a minute.... My answer choices are:

cos x - 4 cos x sin2x

-sin3x + 2 sin x cos x

-sin2x + 2 sin x cos x

2 sin2x cos x - 2 sin x cos x

So I was wrong?

Answer 19

we can alternatively come from sinx to cosx by using first principle..do you know it ?

Answer 20

I'm terribly sorry, but I'm confused, may you explain more.

By the way, the answer I received was cos x - 4 cos x sin2x ; i just want to know how they got it like that.

Answer 21

like a stated before, there are a number of different ways to approach this thing, and there is no one standard rewriting of it.

Answer 22

cos x - 4 cos x sin^2 x

cos x - 4 cos x (1-cos^2(x))

cos x - 4 cos x + 4cos^3(x)

-3cos x + 4cos^3(x)

4cos^3-3cosx, which is what the final we came up with before

so just work it backwards into that ....

Answer 23

Ok, thanks!