Amplitude
Half the distance from peak to trough.
Key idea
Half the distance from peak to trough.
In depth
For y = A sin(x) or A cos(x), the amplitude |A| is half the distance between the maximum and minimum. It scales the wave vertically; a negative A flips it.
Worked example
y = −3 sin x oscillates between −3 and 3, amplitude 3, and is flipped.
Formula
Real-world uses
- Measuring the loudness of a sound wave or the strength of a radio signal
Common mistake
Reporting the amplitude as the full height from minimum to maximum.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Amplitude?
Half the distance from peak to trough. It is a topic at the intermediate level in Trigonometry.
What is the formula for Amplitude?
The key formula is y = A sin(x).
Where is Amplitude used in real life?
Real-world examples: Measuring the loudness of a sound wave or the strength of a radio signal.
What should I learn before Amplitude?
Make sure you are comfortable with Graph of Tangent, the previous topic in Trigonometry.
What is a common mistake with Amplitude?
Reporting the amplitude as the full height from minimum to maximum.
How can I practise Amplitude?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Amplitude?
Move on to Period and Frequency next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.