Math Problem Statement

Sine Graph

Given A sin bx Amplitude = | a | Period = 2pi/B

Amp = 5 Preriod = 2pi / 2 = pi

Graph this problem

Solution

Here's the graph of the sine function 5sin(2x)5 \sin(2x), with:

  • Amplitude: 5 (the maximum value the graph reaches is 5 and the minimum is -5).
  • Period: 2π2=π\frac{2\pi}{2} = \pi, meaning the graph completes one full cycle every π\pi units along the x-axis.

Would you like any more details or have any further questions?

Here are some related questions:

  1. What happens to the sine graph if we change the amplitude to a negative value?
  2. How does the sine graph behave when the period increases?
  3. What are the key differences between sine and cosine graphs?
  4. How do phase shifts affect the sine graph?
  5. What are the applications of sine waves in real-life scenarios?

Tip: The period of a sine function is always determined by the coefficient BB in sin(Bx)\sin(Bx). The larger BB is, the shorter the period becomes!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Functions
Graphing Trigonometric Functions

Formulas

Amplitude = |a|
Period = 2π / B

Theorems

Sine Wave Properties
Periodic Functions

Suitable Grade Level

Grades 10-12