Problem 13 - Precalculus: A Concise Course

Question

Find the period and amplitude. $$ y=3 \sin 10 x $$

Step-by-Step Solution

Answer

The amplitude of the function \(y=3 \sin 10x\) is 3 and the period is \( \frac{\pi}{5}\)

Step 1: Identify the amplitude

To find the amplitude of the function, look at the coefficient of the sine function. In this equation, \(y=3 \sin 10x\), the coefficient is 3, so the amplitude is 3.

Step 2: Identify the Period

To find the period of the function, use the formula \( \frac{2\pi}{B}\), where B is the coefficient of x in the sine function. Here, the coefficient B is 10, so the period is \( \frac{2\pi}{10}\) which simplifies to \( \frac{\pi}{5}\).