Harmonics & Small Angle Approximation

Question 1

Harmonics - What is the formulae?

Answer 1

Rsin(x + a)

Question 2

Harmonics - How do you calculate R and a?
Example = 3sinx + 4cosx

Answer 2

Equation (example) = 3sinx + 4cosx
Rsin(x + a) = Rsinxcosa + Rsinacosx
………………= Rcosa = 3 . Rsina = 4
………………= Rsina/Rcosa = 4/3
………………= tana = 4/3 . a = 53.1
………………= R = /4^2 + 3^2 = 5
3sinx + 4cosx = 5sin(x + 53.1)

Question 3

Harmonics - What is the maximum?

Answer 3

The value of R

Question 4

Small Angle Approximation - what does SinO equal?

Answer 4

SinO = O

Question 5

Small Angle Approximation - What does CosO equal?

Answer 5

CosO = 1 - (O^2)/2

Question 6

Small Angle Approximation - What does TanO equal?

Answer 6

TanO = O

Question 7

Small Angle Approximation - When do you use Small Angle Approximation?

Answer 7

When O is small and measured in radians