Polar Graphing Calculator

What Is a Polar Graph?

A normal graph uses x and y. A polar graph uses two other numbers: r and theta. The angle theta says which way to point, and r says how far to go from the center. Together they place a point.

Imagine a clock hand. Theta is the direction the hand points. R is the length of the hand. As theta turns from 0 to 360 degrees, the tip of the hand draws a curve. That curve is the polar graph.

Polar graphs are best for shapes that turn around a center: spirals, flowers, and circles. These shapes are hard to draw with x and y, but easy with r and theta. That is why precalculus and calculus classes teach polar form.

How to Graph a Polar Function

1. Switch to polar mode. Set the calculator to polar form so it reads r as a function of theta.
2. Type your function. For example, type r = 2 cos(3θ). That draws a rose with three petals.
3. Set the theta range. Start with 0 to 2π (360 degrees). If the curve looks cut off, make the range bigger.
4. Press GRAPH. The curve appears. Use TRACE to move along it and read r and theta at each point.

If the graph looks wrong, check two things: the mode (it must be polar, not function mode) and the theta step (a smaller step draws a smoother curve). Most mistakes come from one of those two settings.

Polar Curves to Try First

• Circle — r = 2. A circle with radius 2 around the center. The simplest polar graph.
• Cardioid — r = 1 + cos(θ). A heart shape. It is the classic first polar curve in class.
• Rose with 3 petals — r = 2 cos(3θ). Three petals, each the same size. Change the 3 to a 4 and count the petals again.
• Rose with 4 petals — r = 2 sin(2θ). Four petals. The number in front of theta sets the petal count.
• Spiral — r = θ. As theta grows, r grows, and the curve winds outward like a snail shell.
• Lemniscate — r² = 4 cos(2θ). A figure-eight lying on its side.

Try the rose first. Change the number of petals and watch the flower change. Then try the spiral and the cardioid. Each one shows a different idea about how r and theta work together.

Polar vs Rectangular Graphing

Both forms draw the same plane. They just use different rules. Some shapes are simple in one form and hard in the other. A circle around the center is r = 2 in polar form, but a square root in rectangular form. A straight line is simple in rectangular form and harder in polar form.

For normal functions, use the function graphing calculator. For surfaces with two inputs, use the 3D graphing calculator. For the classic school layout, use the TI-84 calculator online.

Specialized Graphing Tools

Need a different view? These tools work the same way and are all free.

Frequently Asked Questions