https://file.aiquickdraw.com/mathbot/file/1725474566106sxjf3mwh.jpg

The problem involves determining the period of a trigonometric function \( f(x) = \sin(4x) \) using the general formula for the period of a sine function, which is given as:

\[
T = \frac{2\pi}{|b|}
\]

where \( b \) is the coefficient of \( x \) inside the sine function.

Given the function \( f(x) = \sin(4x) \), the coefficient \( b = 4 \). Thus, the period \( T \) can be calculated as:

\[
T = \frac{2\pi}{4} = \frac{\pi}{2}
\]

The correct answer to the question is therefore **\(\frac{\pi}{2}\)**.

Would you like further details on how the period of trigonometric functions is derived, or do you have any additional questions? Here are five related questions that might interest you:

1. How do you determine the period of a cosine function?
2. What happens to the period of \( \sin(kx) \) as \( k \) increases?
3. How do amplitude and period affect the graph of a sine function?
4. Can you explain the difference between frequency and period in trigonometric functions?
5. How does the phase shift impact the graph of a sine function?

**Tip:** When dealing with trigonometric functions, remember that the period is inversely related to the coefficient of \( x \) within the function.

The period of the following trigonometric function \( f(x) = \sin(4x) \) can be determined using the formula \( T = \frac{2\pi}{|b|} \). What is the period of \( f(x) \)?

Calculate the period of the sine function \( f(x) = \sin(4x) \) using the period formula \( T = \frac{2\pi}{|b|} \). This problem is ideal for students in Grades 10-12, covering key trigonometric concepts and periodic functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation