Trigonometric identities using frequency domain techniques: With practice, it is easier to derive most trigonometric identities than it is to look them up

The engineer is always learning procedures and techniques that make the solving of certain types of problems easier. These techniques often use simplification procedures that not only simplify the analysis, but also transform the problem so that it can be solved using familiar techniques. A good example of this is the solution of electrical circuits where the sources are sinusoidal. The set of integral-differential equations describing the circuit is transformed into a set of simultaneous algebraic equations involving complex numbers. The writing and solving of these equations deal with techniques that are already a familiar part of the engineer's bag-of-tricks. The circuit is transformed into what is called the “frequency domain,” and the emphasis is transformed into one of learning how to deal with complex numbers and complex functions.