# How to find amplitude and period of a graph

## Amplitude, Period, Phase Shift and Frequency

How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift From a Graph

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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.

Every sine function has an amplitude and a period. Amplitude is the distance between the center line of the function and the top or bottom of the function, and the period is the distance between two peaks of the graph, or the distance it takes for the entire graph to repeat. You can find both the amplitude and period of a sine graph without going through the entire process of graphing just by looking at the equation. The generalized equation for a sine graph is as follows:. Remember that we are looking at our functions in terms of radians instead of degrees.

Search Updated February 2nd, In this webpage, you will learn how to graph sine, cosine, and tangent functions. The graphs of trigonometric functions have several properties to elicit. To be able to graph these functions by hand, we have to understand them. Before we progress, take a look at this video that describes some of the basics of sine and cosine curves. The video in the previous section described several parameters. This section will define them with precision within the following table.

Easy to understand trigonometry lessons on DVD. Try before you commit. The variable b in both of the following graph types affects the period or wavelength of the graph. The period is the distance or time that it takes for the sine or cosine curve to begin repeating again. Here's an applet that you can use to explore the concept of period and frequency of a sine curve.

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.

## Graphing Trigonometric Functions

Finding features from graph. Given the graph of a sinusoidal function, we can analyze it to find the midline, amplitude, and period. Consider, for example, the.
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1. Keith G. says:

2. Benjamin B. says:

All Together Now! We can have all of them in one equation: y = A sin(B(x + C)) + D. amplitude is A; period is 2?/B; phase shift is C (positive is to the left); vertical.

3. Peter L. says:

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