Graphing Trigonometric Functions
How To Find The Amplitude, Period, Phase Shift, and Midline Vertical Shift of a Sine Cosine Functionand
Learning Objective s. Periodic Functions. This change does not affect the graphs; they remain the same. You know that the graphs of the sine and cosine functions have a pattern of hills and valleys that repeat. The length of this repeating pattern is.
Let's see what vocabulary is needed to discuss the graphs of trigonometric functions. The midline is affected by any vertical translations to the graph. The period may also be described as the distance from one "peak" max to the next "peak" max. A sinusoid is the name given to any curve that can be written in the form. A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. The midline is parallel to the x -axis and is located half-way between the graphs maximum and minimum values.
Intro Amp. Shift Phase Shift. You've already learned the basic trig graphs. We can transform and translate trig functions, just like you transformed and translated other functions in algebra. This function has an amplitude of 1 because the graph goes one unit up and one unit down from the midline of the graph. Do you see that this second graph is three times as tall as was the first graph? The amplitude has changed from 1 in the first graph to 3 in the second, just as the multiplier in front of the sine changed from 1 to 3.
Amplitude, Period, Phase Shift and Frequency
How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift From a Graph