A function is described as a relation that has one output value for every permissible or possible input value. The number “T” is the period of a function. If the number is fixed and

\begin{array}{l} θ \end{array}

is an angle we have the following periodic formula. The function sine and cosine have a period 2

\begin{array}{l} π \end{array}

. Some of the trigonometry periodic functions are given below:

S i n (ω θ) \Rightarrow T = \frac{2 π}{ω}

C o s (ω θ) \Rightarrow T = \frac{2 π}{ω}

T a n (ω θ) T = \frac{π}{ω}

Solved Example

Question: Find the period of the function

\begin{array}{l} c o s \end{array}

\begin{array}{l} \frac{x}{3} \end{array}

Solution: Let y =

\begin{array}{l} c o s \end{array}

\begin{array}{l} \frac{x}{3} \end{array}

Using the period formula,

T =

\begin{array}{l} \frac{2 π}{ω} \end{array}

The multiple of x =

\begin{array}{l} \frac{1}{3} \end{array}

\begin{array}{l} ω \end{array}

T =

\begin{array}{l} \frac{2 π}{\frac{1}{3}} \end{array}

= 6

\begin{array}{l} π \end{array}

Hence, the period of the function

\begin{array}{l} c o s \end{array}

\begin{array}{l} \frac{x}{3} \end{array}

is 6

\begin{array}{l} π \end{array}

Solved Example

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