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More Lessons on Finding An Equation for Sine or Cosine Graphs

More Algebra 2 Lessons

More Trigonometric Lessons

Videos, worksheets, games and activities to help Algebra 2 students learn how to find the equation of a given sine or cosine graph.

We have included a tool that with plot the sine graph f(x) = A sin(B(x-h))+ k, given the values A, B, h and k. Use it to check your answers.

The following diagram shows how to find the equation of a sine graph. Scroll down the page for examples and solutions.

**Find an Equation for the Sine or Cosine Wave**

When finding the equation for a trig function, try to identify if it is a sine or cosine 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. If the period is more than 2π then B is a fraction; use the formula period = 2π/B to find the exact value.

3. Find any phase shift, h.

**How to determine the equation of a sine and cosine 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.

**Writing equation of sin and cos graph**

Example:

Find the equation of the given graph in terms of sine and cosine.**Trigonometry: Finding an Equation from a Graph**
**Determining the equation of a trigonometric function**

Determining the amplitude and period of sine and cosine functions.**How to come up with the equation of a sin/cos function when given the graph?**
**How to Get Equation of a Sine Curve?**
**How to identify the graph of a stretched cosine curve?**

This video demonstrates how to stretch and shrink the sine and cosine curves.**Finding the equation of Sine or Cosine given its graph**

### Sine Graph Calculator

Enter in the values for f(x) = Asin(B(x-h))+k into the sine graph calculator to check your answer.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons on Finding An Equation for Sine or Cosine Graphs

More Algebra 2 Lessons

More Trigonometric Lessons

Videos, worksheets, games and activities to help Algebra 2 students learn how to find the equation of a given sine or cosine graph.

We have included a tool that with plot the sine graph f(x) = A sin(B(x-h))+ k, given the values A, B, h and k. Use it to check your answers.

The following diagram shows how to find the equation of a sine graph. Scroll down the page for examples and solutions.

When finding the equation for a trig function, try to identify if it is a sine or cosine 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. If the period is more than 2π then B is a fraction; use the formula period = 2π/B to find the exact value.

3. Find any phase shift, h.

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.

Example:

Find the equation of the given graph in terms of sine and cosine.

Determining the amplitude and period of sine and cosine functions.

This video demonstrates how to stretch and shrink the sine and cosine curves.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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