We know trigonometric functions are periodic functions. Sinx and cos x are periodic functions with period 2π or 360° . But tan and cot remain unchanged when x is increased by π or 180° .
So, they are periodic functions with period π.


The general form of the sine function is y = A sinB(x - C) + D
Here, the period is 2π/IBI.

The general form of the cosine function is y = A cosB(x - C) + D
We know cosine functions are identical to the sine functions. So, the period of cosine function is also 2π/IBI.
But for a tangent function. It is π instead of 2π because the period of tan x is π.
If the general form of a tangent function is y = A tanB(x - C)+ D,
its period is π/IBI

There fore, the value of B is the key factor in determining the period of tangent functions. Change in its value changes horizontal stretching. When drawing the graph we have to “stretch” or ;“shrink” the graph horizontally by a factor of B.
Also, the period is unchanged by vertical scaling or shifting or by horizontal shifting.