"They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."
The ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Unit Circle: A circle centered at the origin of the coordinate plane with radius 1, used to define the values of trigonometric functions.
Sine and cosine functions: Two of the six trigonometric functions. The sine function gives the y-coordinate of a point on the unit circle while cosine function gives the x-coordinate.
Periodicity: The property of a trigonometric function that repeats its values at regular intervals.
Amplitude: The maximum value of the function from the mean (average) value.
Period: The shortest interval over which the function looks the same as one full cycle.
Phase shift: A horizontal shift in the graph of a trigonometric function caused by a change in the starting point.
Cotangent, secant, and cosecant functions: The remaining three of the six trigonometric functions. The cotangent function is the reciprocal of the tangent function, the secant function is the reciprocal of the cosine function, and the cosecant function is the reciprocal of the sine function.
Graphing Tangent Functions: Plotting the values of the tangent function on a coordinate plane.
Inverse tangent function: The inverse function of the tangent function, used to find angles when given the ratio of the two sides of a right triangle.
Applications of tangent function: Finding the height or distance of an object that is not directly measurable using tangent function.
"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."
"They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis."
"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."
"This allows extending the domain of sine and cosine functions to the whole complex plane."
"Each of these six trigonometric functions has a corresponding inverse function."
"They are widely used for studying periodic phenomena through Fourier analysis."
"They are among the simplest periodic functions."
"They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others."
"geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used."
"They are widely used in all sciences that are related to geometry, such as navigation."
"Their reciprocals are respectively the cosecant, the secant, and the cotangent."
"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."
"Modern definitions express trigonometric functions as infinite series or as solutions of differential equations."
"The trigonometric functions... relate an angle of a right-angled triangle to ratios of two side lengths."
"They are among the simplest periodic functions."