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- Dictionarytrig·o·no·met·ric func·tion
noun
- 1. a function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.
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Learn what trigonometric functions are and how they relate to the angles and sides of a triangle. Find out the formulas, identities, graphs and examples of sine, cosine, tangent, cotangent, secant and cosecant functions.
- Sine Function
Sine function is one of the three primary functions in...
- Sine Function
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.
- Right Triangle Definition
- Unit Circle Definition
- Trigonometric Function Values For The Special Angles
- Reference Angle
- Trigonometric Functions Are Periodic Functions
- Trigonometric Functions Are Odd Or Even
- Inverse Trigonometric Functions
- Graphs of The Trigonometric Functions
The output of a trigonometric function is a ratio of the lengths of two sides of a right triangle. Consider an angle θ as one angle in a right triangle. The following are the definitions of the trigonometric functions. These functions are often written in their abbreviated forms. The terms used to describe the sides of a right triangle are the hypo...
Trigonometric functions can also be defined as coordinate values on a unit circle. A unit circle is a circle of radius 1 centered at the origin. The right triangle definition of trigonometric functions allows for angles between 0° and 90° (0 and in radians). Using the unit circle definitions allows us to extend the domain of trigonometric functions...
The values of trigonometric functions can be found through the coordinate values of the intersections on a unit circle. While we can find the value of any of the trigonometric functions for any value of θ, there are some angles that are more frequently used in trigonometry and worth memorizing. The following is a list of the sine, cosine, and tange...
Acute angles in the first quadrant can be used to determine the values of trigonometric functions of angles in other quadrants. These angles are called reference angles since we will reference their values to determine other values. It is always the smallest angle (with reference to the x-axis) that can be made from the terminal side of an angle. T...
A periodic function is a function, f, in which some positive value, p, exists such that f(x+p) = f(x) for all x in the domain of f, p is the smallest positive number for which f is periodic, and is referred to as the period of f. All 6 trigonometric functions are periodic functions. No matter what point we start at on the unit circle, if we travel ...
An odd function is a function in which -f(x)=f(-x). It has symmetry about the origin. An even function is a function in which f(x)=f(-x) meaning that reflecting the graph across the y-axis will yield the same graph. Of the 6 trigonometric functions, sine, tangent, cosecant, and cotangent are odd functions. Cosine and secant are even functions. Ther...
The inverse trigonometric functions are the inverse functions of the trigonometric functions. Specifically, they are arcsine, arccosine, arctangent, arccosecant, arcsecant, and arctangent. The input of the inverse trigonometric functions is an angle's trigonometric ratios, and its output is the angle: The inverse trigonometric functions are also wr...
The figure below shows the graphs of several periods of the six trigonometric functions. Refer to the sine, cosine, and tangentpages for an in-depth explanation on how to graph trigonometric functions that have undergone certain transformations (the same explanations apply to cosecant, secant, and cotangent, with minor differences).
The main functions in trigonometry are Sine, Cosine and Tangent. They are simply one side of a right-angled triangle divided by another. For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)
- Introduction to radians. Intro to radians. (Opens a modal) Radians & degrees. Degrees to radians. Radians to degrees.
- The unit circle definition of sine, cosine, & tangent. Unit circle. (Opens a modal) The trig functions & right triangle trig ratios. Trig unit circle review.
- The graphs of sine, cosine, & tangent. Graph of y=sin(x) (Opens a modal) Graph of y=tan(x) Intersection points of y=sin(x) and y=cos(x)
- Basic trigonometric identities. Sine & cosine identities: symmetry. (Opens a modal) Tangent identities: symmetry. Sine & cosine identities: periodicity.
The trigonometric functions relate the angles in a right triangle to the ratios of the sides. Given the following triangle: \hspace {4cm} the basic trigonometric functions are defined for 0 < \theta < \frac {\pi} {2} 0 < θ < 2π as.
The Six Basic Trigonometric Functions. Trigonometric functions allow us to use angle measures, in radians or degrees, to find the coordinates of a point on any circle—not only on a unit circle—or to find an angle given a point on a circle. They also define the relationship between the sides and angles of a triangle.
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