Question

Show sin 4θ = 4sin θ cos θ cos 2 θ

Answer 1

do you know double angle formulas?

Answer 2

not really because m confused with it

Answer 3

but you have been 'taught' them in class?

Answer 4

im teaching myself right now

Answer 5

http://www.sosmath.com/trig/Trig5/trig5/trig5.html
this can help

Answer 6

okay, but what do i do to with the whole equation

Answer 7

im really confused with this part

Answer 8

so how I would do this is to split up the sin(4theta) into this
\[\sin(2x) \] where x= 2theta

Answer 9

if you want me to keep going just say so, but after every step I do I'm going to give you the chance to pick it up and do it yourself.

Answer 10

so what will the new equation look like if we use sin instead of cos

Answer 11

I'm manipulating only the left side. that's how these kinds of problems work, you only mess with one side.

Answer 12

I'll type out a step or two in order.

Answer 13

\[\sin(4\theta)\]
which we then alter to become

\[\sin(2x)\]
then we use the double angle formula to get

2sin(x)cos(x)

then we remember that x = 2theta
and rewrite it like this
\[2\sin(2\theta)\cos(2\theta)\]
got it from here?

Answer 14

would we equal it to 1 and bring it to the other side

Answer 15

would sin 4θ=4sinθcosθcos 2θ become
sin2 θ=2sin(2θ)cos(2θ)