# How do you find the equation of a sinusoidal function from a graph?

## How do you find the equation of a sinusoidal function from a graph?

To find the equation of sine waves given the graph:

1. Find the amplitude which is half the distance between the maximum and minimum.
2. Find the period of the function which is the horizontal distance for the function to repeat.
3. Find any phase shift, h.

## What are the 5 key points when graphing a sinusoidal function?

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

What are the key points of a function?

Key Points

• A function can only have one output, y , for each unique input, x .
• If a vertical line intersects a curve on an xy -plane more than once, then for one value of x the curve has more than one value of y, and the curve does not represent a function.

How do you find the phase shift of a graph?

To find the phase shift from a graph, you need to:

1. Determine whether it’s a shifted sine or cosine.
2. Look at the graph to the right of the vertical axis.
3. Find the first:
4. Calculate the distance from the vertical line to that point.
5. If the function was a sine, subtract π/2 from that distance.

### What is the period of a graph?

The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. Any part of the graph that shows this pattern over one period is called a cycle. For example, the graph of on the interval is one cycle.

### How do I graph trigonometric functions?

To use these features when graphing trigonometric functions, follow these steps: Put the calculator in Function and Radian mode. Press [MODE]. Enter your trigonometric functions into the Y= editor. See the first screen. Press [ZOOM][7] to graph the function. [ZOOM][7] invokes the ZTrig command that graphs the function in a viewing window in which

What is the equation for a sine graph?

The general equation of a sine graph is y = A sin(B(x – D)) + C. The general equation of a cosine graph is y = A cos(B(x – D)) + C. Example: Given a transformed graph of sine or cosine, determine a possible equation.

How do you calculate sine wave?

In general, a sine wave is given by the formula In this formula the frequency is w. Frequency used to be measured in cycles per second, but now we use the unit of frequency – the Hertz (abbreviated Hz). One Hertz (1Hz) is equal to one cycle per second.