In mathematics , the trigonometric functions also called circular functions , angle functions or goniometric functions   are real functions which relate an angle of a right-angled 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 , geodesy , and many others. They are among the simplest periodic functions , and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine , the cosine , and the tangent. Their reciprocals are respectively the cosecant , the secant , and the cotangent , which are less used. Each of these six trigonometric functions has a corresponding inverse function called inverse trigonometric function , and an equivalent in the hyperbolic functions as well.
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Right Triangle Trigonometry - Algebra and Trigonometry | OpenStax
Last time we looked at some details that are rarely mentioned in stating the conventions for interpreting algebraic expressions. Much of the same is true of logarithms. If trig functions were written using the normal notation for functions, e. All a linguist can do to understand a language is to study how it is used by its speakers. And trigonometry is a dialect of its own!
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How steep is this hillside and will it fail? How high is that mountain? These sorts of questions pop up all over in geosciences - from plate tectonics to maps to ocean waves, and they require you to find either an angle or a distance.