Want to know more about trig function?

Definition of trigonometric functions is given as it is a function that relates the angle and sides of the right-angle triangle. In simple words we can define trigonometric functions as ratios of sides of right-angle triangle.

Now we see different kind of trigonometric functions. In which we covers trig functions like sine, cosine, tangent, cosecant, secant, cotangent and also gives trigonometric function definition in a form of mathematical formula.

Here is a list of trigonometric functions,

1) sine function :

sine is one of the fundamental trig function. As shown in below figure for angle θ, sinθ equals the ratio of opposite side of the angle θ to the hypotenuse of right-angle triangle.

trig function 

sin θ = opposite's length / hypotenuse's length

2) cosine function :

cosine is the fundamental trigonometric function.
cosθ equals the ratio of adjacent side of the angle θ to the hypotenuse of right-angle triangle.

cos θ = adjacent's length / hypotenuse's length

3) tangent functions :

tangent is ratio of sine and cosine function.

tan θ = sin θ / cos θ

4) cosecant functions :

cosecant is a inverse of sine.

cosecant θ = 1 / sin θ

5) secant function :

secant is a inverse of cosine.

secant θ = 1 / cosine θ

6) cotangent function :

cotangent is a inverse of tangent.

cotangent θ = 1 / tangent θ

All about graphing trigonometric functions

The process of graphing trigonometric functions is simple. First of all prepare trigonometric tables by finding values of trig functions for some standard value of angles. All graphs of trigonometric functions shown below.
graphing trigonometric functions

Method for preparing trigonometric functions table

Trigonometric functions table are very useful in process of graphing trig functions. Below is a table which shows values of all trigonometric functions for particular angle.
Trigonometric functions table

Now the question arise that what are applications of trigonometric functions?? They are used for finding height of tower or buildings or mountains and also distance in sea or desert or mountains area.

We will get more idea trig function by solving trigonometric functions. In which we start with adding trigonometric functions. If angles are same addition is very for two trig functions.

Example 1 : add two trigonometric functions 4sin3A and 5sin3A.

Ans : 4sin3A + 5sin3A = 9sin3A

Example 2 : Multiply two trigonometric functions 2sin2A and 3sin3A.

Ans : 2sin2A * 3sin3A = (2*3)sin2+3A = 6sin5A

The right angle triangle and trigonometric table are very useful in evaluating trigonometric functions. Here some trigonometric functions problems are shown to clear this concept.
trigonometric functions problems

evaluating trigonometric functions

And at last we learn about differentiation of trigonometric functions which are shown below,
differentiation of trigonometric functions


More topics in Trigonometric Functions
Sine Function Cosine Function
Tangent Function Cosecant Function
Secant Function Cotangent Function
The Inverse Sine Function The Inverse Cosine Function
The Inverse Tangent Function Inverse Cosecant Function
Inverse Secant Function Inverse Cotangent Function
Graph of the Tangent Function
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