Question

Can you please help me understand the double-angle formulas better? I see that sin(2x) = (2)sin(x)cos(x), but what if I have sin(5x)? How do I apply the double-angle formulas then?

Answer 1

You can use the fact that 5x = 2x + 3x

Answer 2

you are unable to directly apply the double angle formula here because 5 isnt even

Answer 3

yeah but you can also use this sin(A+B) = sinAcosB + sinBcosA, in addition to the hint i gave earlier.

Answer 4

@ByteMe so would it be sin(5x) = sin(2x)cos(3x) + sin(3x)cos(2x)?
sin(5x) = 2sin(x)cos(x)cos(3x) + sin(3x)(cos^2(x) - sin^2(x))
....and so on?

@Skaematik Does that mean that there is a simpler solution for sin(4x) ?

Answer 5

@JohnT , that's correct ^^^

Answer 6

hmmm..., maybe 5x = 4x + x would have been better then you could use double angle formula with 4x = 2*2x

Answer 7

Sin4x

let 2x = A

sin4x = sin2A
sin2A = 2sinAcosA
subbing 2x = A -> sin4x = 2sin2xcos2x

Answer 8

Thanks @Skaematik