## Appendix E. Mathematical Relationships

### Trigonometric Functions

sin^{2} *θ* + cos^{2} *θ* = 1

sin(*θ* ± φ) = sin *θ* cos *θ* ± cos*θ* sin *φ*

sin 2*θ* = 2 sin *θ* cos*θ*

cos 2*θ* = cos^{2} *θ* – sin^{2} *θ*

### Euler’s Identities

*e*^{iθ} = cos*θ* + *i*sin *θ*

*e*^{–iθ} = cos *θ* – *i* sin *θ*

### Quadratic Equation (*ax*^{2} + *bx* + *c* = 0)

### Derivatives

### Indefinite Integrals

### Definite Integrals

### Geometric Series

### Taylor Series ...