Question

Explain what it means to say that the period of a function is $180°$.

Short answer

It means that the graph of the function repeats itself after an interval of $180{}^{\circ }\text{or}\pi$.

Step-by-step solution

Step 1. Write down the given information.

The given statement is to explain that the period of the function is $180°$.

Step 2. Explanation.

The definition of period or periodicity of a function means that the graph of a function repeats itself after a specific interval. Therefore, if the given function has a period of $180°$ then it means that the graph of the function repeats itself after an interval of $180{}^{\circ }\text{or}\pi$. For example, the period of the sine and cosine function is $360{}^{\circ }\text{or}2\pi$ which means that the graph of sine and cosine function will repeat after an interval of $360{}^{\circ }\text{or}2\pi$. And second example is of tangent and cotangent function whose period is $180{}^{\circ }\text{or}\pi$ which means that the period of tangent and cotangent function will repeat itself after an interval of $180{}^{\circ }\text{or}\pi$.

Step 3. Conclusion.

It means that the graph of the function repeats itself after an interval of $180{}^{\circ }\text{or}\pi$.