Polar Graphs: Rose Curves r = a·sin(nθ)
A rose curve r = a·sin(nθ) has n petals when n is odd and 2n petals when n is even, each of length a; r = 3 sin(4θ) has 8 petals of length 3.
At a glance
| What it is | Graph polar equations online, like the rose curve r = 3 sin(4θ). Learn how many petals a rose has. Free polar graphing calculator. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Petals (n odd) | n |
|---|---|
| Petals (n even) | 2n |
| Petal length | |a| |
| Polar to Cartesian | x = r·cos(θ), y = r·sin(θ) |
How do you type a polar equation?
Start the equation with r = and use θ (type "theta" or use the θ key). Plotline sweeps θ from 0 to 2π to draw the whole curve.
How to use it in Plotline
- The graph of r = 3 sin(4θ) is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
How many petals does r = 2 sin(3θ) have?
Three. For r = a·sin(kθ) the rose has k petals when k is odd and 2k petals when k is even, so sin(3θ) gives 3 petals and sin(4θ) gives 8. The value of a sets how long each petal is.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
Related
- Sine graph – Graph y = sin(x) online.
- Circle – Graph circles online from their equation.
- Cosine graph – Graph y = cos(x) online and compare it with sin(x).
Free calculators
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- Basic Calculator – A simple, free online calculator for add, subtract, multiply, divide, percent, square and square root.
- Matrix Calculator – Free matrix calculator: determinant, inverse, multiplication, transpose, RREF, rank, trace and powers, with exact fractions.
Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.