Stretching/compressing factor

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.

5 Must Know Facts For Your Next Test

1. The stretching factor affects the amplitude of sine and cosine functions, represented as $y = a \sin(bx)$ or $y = a \cos(bx)$.
2. A horizontal compressing factor affects the period of trigonometric functions, calculated as $\frac{2\pi}{b}$ for sine and cosine.
3. $a > 1$ vertically stretches the graph while $0 < a < 1$ compresses it.
4. $b > 1$ horizontally compresses the graph while $0 < b < 1$ stretches it.
5. 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 $y = \tan(bx)$.

Related terms

Amplitude: The maximum distance from the midline to the peak (or trough) of a trigonometric function; affected by vertical stretching/compressing factors.

Period: The horizontal length over which a trigonometric function completes one full cycle; affected by horizontal stretching/compressing factors.

$Phase\ Shift$: $Horizontal\ shift\ along\ x-axis$ due to addition/subtraction inside trigonometric functions; does not affect stretching/compressing factors.