By examining the unit circle, one can establish the following properties of the trigonometric functions.
When … See more

These are also known as the angle addition and subtraction theorems (or formulae).
The angle difference identities for and can be derived from the angle sum versions by substituting for and using the facts that and . They can al… See more

Formulae for twice an angle.
Formulae for triple angles.
Formulae for multiple angles.
The Chebyshev method is a recursive algorithm for finding the nth multiple angle formula kn… See more

The product-to-sum identities or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's fo… See more

For some purposes it is important to know that any linear combination of sine waves of the same period or frequency but different phase shifts is also a sine wave with the same period or frequency, but a different phase shift… See more