# Cosine Function as one of the trigonometric function

The right angle triangle has a adjacent side, opposite side and a hypotenuse. The **definition of cosine function** is given as cosine of a angle **θ is equal to ratio of adjacent side and hypotenuse. Lets make ****cosine function ****more clear by below diagram.
**

**The equation of cos function ****is given as****,**

** ****cos***θ*** = ****Adjacent side / Hypotenuse**

## Closer look on graph cosine function

**The process for ****graphing cosine function**** is very simple. For the different values of angle (say angle a) find the value of cosine of that angle (cos(a)). Plot the graph of angle v/s cosine of angle. So this is how ****graph cosine function**** prepared. ****Cosine functions**** value at different value of angle is given below,
**

** ****From above table, the graph of it prepared which looks like,
**

**Some of conclusions from ****cosine function graph ****are,
**

**1. The cosine function repeated after every 2**

*π***interval, so its period is 2**

*π***.**

**2. The cosine function exists for all value of angle, so its domain is from −∞ to +∞.**

**3. The cosine function is always have a value between -1 to +1, so its range is from -1 to +1.**

**4. The cosine function is even function, so cos(-**

*θ***) = cos(**

*θ***).**

**After studying process of ****graphing cos functions****, we will going through ****cosine formulas****.**

** 1) The most commonly and widely usable formula which is also known as Pythagorean identity is,**

** sin**^{2}**x + cos**^{2}**x = 1**

** so, cos**^{2}**x = 1 - sin**^{2}**x**

** 2) The derivative ****formula for cosine function ****is,
**

**3) The Integration formula for it is,
**

**4) The addition and subtraction of two cosine angle is given by,**

** cos(x + y) = cos(x)cos(y) – sin(x)sin(y)**

** cos(x – y) = cos(x)cos(y) + sin(x)sin(y)**

** 5) The multiple angles of cosine can be simplifies as,**

** cos(2x) = cos**^{2}**x – sin**^{2}**x**

** cos(3x) = 4cos**^{2}**(x) - 3cos(x)**

** 6) For divided angle cosine can be simplifies as,
**

**7) Different types of operation on cosine functions,
**

## Video Lesson on Cosine Graph

** **

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