# 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, *sin*θ *equals the ratio of opposite side of the angle θ to the hypotenuse of right-angle triangle.

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

2) cosine function :

cosine is the fundamental trigonometric function. cos*θ *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.

**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.

Now the question arise that what are a**pplications 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 2sin^{2}A and 3sin^{3}A.

Ans : 2sin^{2}A * 3sin^{3}A = (2*3)sin^{2+3}A = 6sin^{5}A

** 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.

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

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