elchapo6762 elchapo6762
  • 07-03-2018
  • Mathematics
contestada

sin 4 theta

hey, how do you simplify sin 4 theta? using double angle theory?

Respuesta :

Mindaka
Mindaka Mindaka
  • 18-03-2018
Yes, you do use double-angle formulas. 
You begin with double-angle formula for sine:

sin(4θ) = sin(2·2θ) = 2·sin(2θ)·cos(2θ)

Then, double-angle formula for sine again:

2·sin(2θ)·cos(2θ) = 2·2·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·cos(2θ)

Then
double-angle formula for cosine:

4·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·(cos²θ - sin²θ)

Last, multiply:

4·sinθ·cosθ·(cos²θ - sin²θ) = 4·sinθ·cos³θ - 4·sin³θ·cosθ




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