Question

Explain the term period as it relates to the graph of a sinusoidal function.

Short answer

The term period represents the value after which the graph of a sinusoidal function starts repeating itself.

Step-by-step solution

Step 1. Concept Used

If $\omega >0$, then the amplitude and period of $y=A\sin \left(\omega x\right)$and $y=A\cos \left(\omega x\right)$are given by

Amplitude$=\left|A\right|$

Period$=\frac{2\mathrm{\pi }}{\omega }$

Step 2. Find what period represents

The period of a cyclic function gives the x values after which the function starts repeating.

Sinusoidal functions of the form $y=A\sin \left(\omega x\right)$or $y=A\cos \left(\omega x\right)$where $\omega >0$are cyclic functions and their period is denoted as $T=\frac{2\mathrm{\pi }}{\omega }$.

This means that the sinusoidal functions will start repeating after every $\frac{2\mathrm{\pi }}{\omega }$, and its one cycle is given by the interval$\left[0,\frac{2\mathrm{\pi }}{\omega }\right]$.