"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."
The reciprocal of the cosine function.
Unit Circle: The unit circle is used in trigonometry to understand the angles and lengths of the secant function.
Degrees and Radians: The angles in trigonometry are measured in degrees or radians. A conversion between degrees and radians is important when studying trigonometry.
Pythagorean Theorem: The Pythagorean theorem is a fundamental concept in trigonometry. It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Trigonometric Ratios: Trigonometric ratios define the relationship between the sides of a right triangle and its angles. The three basic ratios are sine, cosine, and tangent, which are related to secant in a specific manner.
Secant Function: The secant function is defined as the reciprocal of the cosine function. It takes an angle as input and produces the ratio of the hypotenuse to the adjacent side of a right triangle.
Domain and Range of Secant Function: The domain of the secant function is all real numbers except where the cosine function is equal to zero. The range of the secant function is all real numbers.
Secant Identities: Secant identities are fundamental trigonometric identities that help simplify equations and solve problems. Some of the important secant identities are reciprocal, Pythagorean, and quotient identities.
Graphs of Secant Function: The graph of the secant function is a periodic curve that oscillates between positive and negative infinity as the angle increases. The graph of the secant function can be used to find the amplitude and period of a function.
Inverse Secant Function: The inverse secant function is the inverse of the secant function. It takes the ratio of the hypotenuse to the adjacent side of a right triangle as input and produces the angle.
Solve Trigonometric Equations: Trigonometric equations are equations that involve one or more trigonometric functions. The secant function can be used to solve equations involving other trigonometric functions, such as sine and cosine.
Sine Function: It describes the y-coordinate of the unit circle when the circle is rotaed by a measured angle from the positive x-axis.
Cosine Function: It describes the x-coordinate of the unit circle when the circle is rotated by a measured angle from the positive x-axis.
Tangent Function: It describes the ratio of the sine and cosine functions at any given angle.
Cotangent Function: It describes the reciprocal of the tangent function.
Secant Function: It describes the reciprocal of the cosine function.
Cosecant Function: It describes the reciprocal of the sine 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."
"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."
"Then 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."
"...and as such are also widely used for studying periodic phenomena through Fourier analysis."
"They are among the simplest periodic functions."
"This allows extending the domain of sine and cosine functions to the whole complex plane..."
"...and the domain of the other trigonometric functions to the complex plane with some isolated points removed."
"They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."
"In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions)..."
"...relate an angle of a right-angled triangle to ratios of two side lengths."
"Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used."
"Modern definitions express trigonometric functions as infinite series or as solutions of differential equations."
"They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."