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Trigonometric Function


									                   Trigonometric Function
Trigonometric Function

In mathematics, the trigonometric functions (also called circular functions) are
functions of an angle.

They are used to relate the angles of a triangle to the lengths of the sides of a
triangle. Trigonometric functions are important in the study of triangles and modeling
periodic phenomena, among many other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. In the
context of the standard unit circle with radius 1, where a triangle is formed by a ray
originating at the origin and making some angle with the x-axis, the sine of the angle
gives the length of the y-component (rise) of the triangle, the cosine gives the length
of the x-component (run), and the tangent function gives the slope (y-component
divided by the x-component).

More precise definitions are detailed below. Trigonometric functions are commonly
defined as ratios of two sides of a right triangle containing the angle, and can
                                       Know More About Trigonometric Identities                                               Page No. : ­ 1/4
equivalently be defined as the lengths of various line segments from a unit circle.
More modern definitions express them as infinite series or as solutions of certain
differential equations, allowing their extension to arbitrary positive and negative
values and even to complex numbers.

Trigonometric functions have a wide range of uses including computing unknown
lengths and angles in triangles (often right triangles). In this use, trigonometric
functions are used, for instance, in navigation, engineering, and physics.

A common use in elementary physics is resolving a vector into Cartesian coordinates.
The sine and cosine functions are also commonly used to model periodic function
phenomena such as sound and light waves, the position and velocity of harmonic
oscillators, sunlight intensity and day length, and average temperature variations
through the year.

In modern usage, there are six basic trigonometric functions, tabulated here with
equations that relate them to one another.

Especially with the last four, these relations are often taken as the definitions of those
functions, but one can define them equally well geometrically, or by other means, and
then derive these relations.

In periodic function we use sine and cosine functions like sound, the light waves,
sunlight intensity and light waves, average moisture, temperature and etc. The
functions which are formed by the ratios of the two sides of any right triangle that
contains the same angles and are defined equivalently as the lengths of different line
segments from any circle are commonly called as trigonometric functions.

                        Read  More About Derivative Of Absolute Value Functions                                                Page No. : ­ 2/4
These functions have assorted applications in the modern world that includes
computing unknown lengths and angles in a right triangle. With this, trigonometric
functions have several applications in the modern science, physics, chemistry and
other fields.

Let’s have an example and see how to do trigonometric functions?

For instance: Solve 1/cosec + sinx?

Solution: Given functions is 1/cosec + sinx

As you know the value of 1/cosec is sinx,

So replace 1/cosec by sinx and we get:

= Sinx+ Sinx,

= 2sinx.

Thus we get the value of 1/cosec + sinx as 2sinx.

Let’s understand how to solve trigonometric function with help of one more example
so that you can easily understand trigonometric functions.

Example: Prove that tanx+ 1/cotx = 2sinx/cosx?

Solution: In order to solve the above given problem you must know the value of the
tan as cot and how we can write the same in different forms.                                            Page No. : ­ 3/4
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