Graph Each Function Using Degrees Calculator

This calculator helps you graph trigonometric and polynomial functions using degree-based angles. The interactive chart displays the function's behavior across a specified range, making it easy to visualize mathematical relationships.

How to Use This Calculator

To graph a function using degrees:

Select the function type from the dropdown menu (sine, cosine, tangent, or polynomial).
For trigonometric functions, enter the amplitude and period values.
For polynomial functions, enter the coefficients for each term.
Set the minimum and maximum values for the x-axis range.
Click "Calculate" to generate the graph and see the function's behavior.

The calculator will display an interactive chart showing the function's curve, with key points marked for reference.

Formula Used

For trigonometric functions:

y = A * sin(ωx) + C
where:
A = amplitude
ω = 2π / period
C = vertical shift (default 0)

For polynomial functions:

y = a₀ + a₁x + a₂x² + ... + aₙxⁿ

The calculator uses these formulas to compute the y-values for each x-value in the specified range.

Worked Examples

Example 1: Sine Function

Graph y = 2 * sin(x) with x from 0 to 360 degrees.

The graph will show a sine wave with amplitude 2, completing one full cycle from 0 to 360 degrees.

Example 2: Polynomial Function

Graph y = x² - 4x + 4 with x from -5 to 5.

The graph will show a parabola opening upwards with its vertex at (2,0).

Interpreting Results

The graph provides several key insights:

For trigonometric functions, you can see the amplitude, period, and phase shift.
For polynomial functions, you can identify the degree, roots, and vertex.
The interactive chart allows you to zoom in on specific areas for detailed analysis.

Use this information to understand the function's behavior and apply it to real-world problems.

FAQ

What types of functions can I graph with this calculator?

You can graph sine, cosine, tangent, and polynomial functions using degree-based angles.

How do I change the range of the graph?

Use the minimum and maximum x-axis value inputs to adjust the range displayed on the graph.

Can I save the graph as an image?

Currently, the calculator does not include save functionality. You can take a screenshot of your browser window to save the graph.