Stretching/compressing factor
from class:
Algebra and Trigonometry
Definition
A stretching/compressing factor in trigonometric graphs is a coefficient that alters the amplitude or period of the function. It can vertically stretch/compress the graph or horizontally stretch/compress it.
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5 Must Know Facts For Your Next Test
- The stretching factor affects the amplitude of sine and cosine functions, represented as $y = a \sin(bx)$ or $y = a \cos(bx)$.
- A horizontal compressing factor affects the period of trigonometric functions, calculated as $\frac{2\pi}{b}$ for sine and cosine.
- $a > 1$ vertically stretches the graph while $0 < a < 1$ compresses it.
- $b > 1$ horizontally compresses the graph while $0 < b < 1$ stretches it.
- The period of tangent and cotangent functions is affected by horizontal stretching/compressing factors, calculated as $\frac{\pi}{b}$.
Review Questions
- How does changing the value of 'a' in $y = a \sin(x)$ affect its graph?
- What is the new period of $y = \cos(3x)$?
- Describe how to find the period of a transformed tangent function given by $y = \tan(bx)$.
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