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.
cosine function

The equation of cos function is given as,

cosθ = 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,
Cosine functions value

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

Some of conclusions from cosine function graph are,

1. The cosine function repeated after every 2π interval, so its period is 2π.
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,

sin2x + cos2x = 1

so, cos2x = 1 - sin2x

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

3) The Integration formula for it is,
Integration formula for cosine function

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) = cos2x – sin2x

cos(3x) = 4cos2(x) - 3cos(x)

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

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

Video Lesson on Cosine Graph


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