# Trig Transformations

- Author:
- Ken Schwartz

- Topic:
- Trigonometry

The four transformations we have applied to functions have special names for trig functions:
"Standard" Transformation:
Trig Transformation: or
The amount of vertical stretch/compression is called Amplitude (A), and is always positive such that A = |a|;
The amount of horizontal stretch/compression is called Frequency ( , "omega") instead of "b";
The , "phi") and is found as . The Phase Shift is the same as the Horizontal Shift when .
The amount of vertical shift is still called k, though it is also sometimes referred to as the "midline".
This app demonstrates the effect of each transformation.

*absolute*amount of horizontal shift is still called h, but the*relative*amount of shift is called Phase Shift (Each slider controls one of the transformations. Notice that the Period (P), the length of one cycle, is inversely proportional to the Frequency ( ) - the higher the frequency, the shorter the period. If the sine function is a sound wave, then the Amplitude (A) corresponds to the volume (loudness), while the frequency corresponds to the pitch. For visible light waves, red has a longer period (lower frequency) than blue (shorter period, higher frequency).
Phase Shift can be a bit confusing, but it measures the horizontal shift in terms of one wavelength (cycle) being radians (or 360 degrees) long, regardless of frequency. So, a 1/4 wavelength phase shift is always radians (or 90 degrees), no matter what the period or frequency is.