In mathematics, the trigonometric functions (also called circular functions, angle functions, or goniometric functions) are real functions that relate an angle of a rightangled triangle to ratios of two side lengths.
They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, and geodesy. They are also among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Given their widespread use, trigonometric functions often find their way into advanced mathematics, requiring the application of techniques seen in calculus, such as differentiation. Differentiation of trigonometric functions is a mathematical process of determining the rate of change of the trigonometric functions with respect to the variable angle.
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