iCoachMath
STEM Excellence Series: Empowering the Next Generation
AMPLITUDE
Amplitude
Definition Of Amplitude
Amplitude is half the distance between the minimum and maximum values of the range of a periodic function with a bounded range.
In other words, for functions of the form y = A sin bθ or y = A cos bθ, the amplitude is |A|.
Examples of Amplitude
Video Examples: Free Math Lessons Sine Graph Amplitude
Solved Example on Amplitude
Ques: Find the amplitude of the function .
Choices:
A. - 4
B. 4
C. 1/2
D. - 3
Correct Answer: B
Solution:
Step 1: Recall that "for functions of the form y = A cos bθ, the amplitude is |A|".
Step 2: So, 4 is the amplitude of the given function.
Quick Summary
- Amplitude is a measure of the height of a wave.
- For y = A sin(x) or y = A cos(x), the amplitude is |A|.
- The amplitude affects the maximum and minimum values of the function.
\[ |A| \]
⚠️ Common Mistakes
- Confusing amplitude with period.
- Forgetting to take the absolute value of A.
- Thinking amplitude affects the horizontal stretch of the graph.
🌍 Real-World Uses
- The amplitude of a sound wave determines its loudness; a larger amplitude means a louder sound.
- In seismology, the amplitude of seismic waves helps measure the magnitude of an earthquake.
- The amplitude of alternating current (AC) voltage affects the brightness of a light bulb connected to the circuit.
📋 Standards Alignment
CCSS.MATH.CONTENT.HSF.TF.B.5
🔗 Related Links
🍎 Teacher Insights
Use real-world examples like sound waves or ocean waves to illustrate the concept of amplitude.🎓 Prerequisites
- Periodic functions
- Sine and cosine functions
- Maximum and minimum values
Check Your Knowledge
Q1: What is the amplitude of the function y = 4 cos(x)?
Q2: What is the amplitude of y = -2 sin(x)?
Frequently Asked Questions
Q: What is the range of a sine function with amplitude A?
A: The range is [-A, A].
Q: How does amplitude affect the graph of a cosine function?
A: It stretches the graph vertically.