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.

Labels: Functions, Trigonometry