"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."
Functions of an angle that describe the relationships between the sides and angles in a right triangle.
Degrees and Radians: This topic covers the two units used to measure angles in trigonometry: degrees and radians.
Trigonometric Ratios: In this topic, you will learn about the three primary trigonometric ratios: sine, cosine, and tangent.
Unit Circle: The unit circle is a circle with a radius of 1 and its center at the origin of the coordinate plane. This topic covers how to use the unit circle to find the values of trigonometric functions.
Trigonometric Identities: This topic deals with identities that relate the values of one trigonometric function to the values of others, such as the Pythagorean identity.
Inverse Trigonometric Functions: Inverse trigonometric functions are used to determine the angle that gives a certain trigonometric ratio.
Trigonometric Equations: Trigonometric equations are equations that involve trigonometric functions. This topic covers how to solve different types of trigonometric equations.
Trigonometric Graphs: This topic covers the graphs of trigonometric functions such as sine, cosine, and tangent.
Complex Numbers and Trigonometry: Complex numbers can be used to represent points in the complex plane, and trigonometric functions can be used to express them.
Applications of Trigonometry: Trigonometry is used extensively in fields such as physics, engineering, and navigation. This topic covers how trigonometry can be used in these areas.
Trigonometric Series: Trigonometric series are infinite series that involve trigonometric functions. This topic covers how to manipulate and use them.
Sine Function: :.
Cosine Function: :.
Tangent Function: :.
Secant Function: :.
"They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."
"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, and an analog among the hyperbolic functions."
"The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles."
"To extend the sine and cosine functions to functions whose domain is the whole real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used."
"The domain of the other functions is the real line with some isolated points removed."
"Modern definitions express trigonometric functions as infinite series or as solutions of differential equations."
"This allows extending the domain of sine and cosine functions to the whole complex plane."
"The domain of the other trigonometric functions is the complex plane with some isolated points removed."
"They are among the simplest periodic functions and are widely used for studying periodic phenomena through Fourier analysis."
"The trigonometric functions (also called circular functions, angle functions or goniometric functions)"
"such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."
"...relate an angle of a right-angled triangle to ratios of two side lengths."
"geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used."
"Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions."
"...extending the domain of sine and cosine functions to the whole complex plane."
"...the domain of the other trigonometric functions to the complex plane with some isolated points removed."
"Modern definitions express trigonometric functions as infinite series or as solutions of differential equations."