There are three types of trigonometric functions, they are:
1- Plane Trigonometric Functions
2- Inverse Trigonometric Functions and
3- Hyperbolic Trigonometric Functions
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With ease, I suppose. The question depends on what you consider easy trigonometric functions.
There are infinitely many types of functions. For example: Discrete function, Continuous functions, Differentiable functions, Monotonic functions, Odd functions, Even functions, Invertible functions. Another way of classifying them gives: Logarithmic functions, Inverse functions, Algebraic functions, Trigonometric functions, Exponential functions, Hyperbolic functions.
Vectors.
Trigonometric identities involve certain functions of one or more angles. These identities are useful whenever expressions involving trigonometric functions need to be simplified.
Yes.