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There are three types of trigonometric functions, they are: 1- Plane Trigonometric Functions 2- Inverse Trigonometric Functions and 3- Hyperbolic Trigonometric Functions
With ease, I suppose. The question depends on what you consider easy trigonometric functions.
Euler published the formula, which relates complex exponentials to trigonometric functions in 1748. See related link.
Vectors.
Trigonometric identities involve certain functions of one or more angles. These identities are useful whenever expressions involving trigonometric functions need to be simplified.