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Chapter 4: Problem 13

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

Short Answer

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

Step by step solution

01

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.
02

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 \( \frac{\pi}{5}\).

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Most popular questions from this chapter

Use a graphing utility to graph the function. Include two full periods. $$ y=-\csc (4 x-\pi) $$

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \csc x=\sqrt{2} $$

Sketch the graph of the function. Include two full periods. $$ y=3 \cot \frac{\pi x}{2} $$

Sketch the graph of the function. Include two full periods. $$ y=\frac{1}{2} \sec \pi x $$

Evaluate the expression without using a calculator. $$ \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right) $$
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