Plotting a Sine Wave

By the end of this lesson you'll be able to:

• Import the math library and use math.sin() to calculate sine values
• Use a for loop with goto() to plot a mathematical function across the canvas
• Adjust the amplitude and color of the wave by changing two variables

Turtle graphics aren't just for shapes — you can use them to plot math functions. The turtle visits hundreds of points along the x-axis, calculates the y-value for each, and connects them with goto(). The result looks like a graph, drawn live.

Welcome to This Lesson!

Did you know Python can draw math? Today you'll plot a sine wave — the shape of ocean waves, sound, and light — right in the browser. Let's code it together!

The Sine Function

The sine function math.sin(angle) takes an angle in radians and returns a value between -1 and 1. A full sine wave goes from 0 up to 1, back down through 0 to -1, and back up to 0 — a smooth S-shaped curve.

Two steps to plot it with turtle: 1. Loop x from -180 to 180 2. Convert x to radians with math.radians(x), then call math.sin() to get y 3. Multiply y by an amplitude (like 80) to scale it up to canvas size 4. Use goto(x, y * amplitude) to move the turtle

import math
for x in range(-180, 180):
    y = math.sin(math.radians(x))
    monty.goto(x, y * 80)

Sample Code

import turtle
import math

monty = turtle.Turtle()
monty.shape('turtle')
monty.speed(10)

amplitude = 80
monty.color('blue')
monty.pensize(2)

monty.penup()
monty.goto(-180, 0)
monty.pendown()

for x in range(-180, 180):
    y = math.sin(math.radians(x))
    monty.goto(x, y * amplitude)

monty.hideturtle()

What Do You Think Will Happen?

The turtle will visit 360 points from x = -180 to x = 179 and draw a line through all of them. What shape do you expect to see? Will it look smooth or jagged? Make your guess — then click Run!

Try It Now

Edit the code below and click Run to see the result right on this page. No account needed — everything runs in your browser.

▶ Run ↻ Reset

Were you right? A smooth S-curve stretching across the canvas — one full cycle of the sine function, scaled to 80 pixels tall.

How It Works

math.radians(x) converts degrees to radians (the unit math.sin() expects). The returned value is between -1 and 1, so multiplying by amplitude (80) stretches it to ±80 pixels — a visible wave.

Starting with penup() and goto(-180, 0) positions the turtle at the left edge of the wave without drawing a line there first. Then pendown() starts the wave at exactly x = -180.

Explanation Table

Line	What it does
import math	Loads the math library (provides sin, cos, radians, etc.)
amplitude = 80	Controls how tall the wave is — larger = taller
math.radians(x)	Converts degrees to radians (required by math.sin)
math.sin(...)	Returns a value between -1 and 1 for that angle
y * amplitude	Scales the value to canvas coordinates
monty.goto(x, y * amplitude)	Moves the turtle to the next point on the curve

Try math.cos() Too

Replace math.sin with math.cos and see how the wave shifts. The cosine wave is identical in shape to sine but shifted left by 90 degrees — so instead of starting at 0 it starts at its peak!

Learning Check

Your Turn — Draw Two Waves

The program below draws one sine wave. Add four lines after the first loop ends to: lift the pen (penup), go back to (-180, 0), lower the pen (pendown), and draw a second loop in 'red' using math.cos instead of math.sin.

▶ Run ↻ Reset

Experiments

Try these changes to the sine wave code. Predict first, then run!

1. Change amplitude = 80 to amplitude = 160. You'll know it worked when the wave is twice as tall and the peaks nearly reach the top of the canvas.

2. Change amplitude = 80 to amplitude = 30. You'll know it worked when the wave is much flatter — almost a straight line.

3. Replace math.sin with math.cos. You'll know it worked when the wave starts at its peak (y = amplitude) instead of at zero.

4. Change range(-180, 180) to range(-360, 360, 2) (step by 2). You'll know it worked when you see two full cycles of the wave across the canvas.

5. Multiply the radians by 2 before passing to math.sin: math.sin(math.radians(x) * 2). You'll know it worked when the wave completes two full cycles in the same x range.

Great Work!

You plotted a mathematical function with turtle — you're writing the kind of code scientists and engineers use to visualize data! Try combining sin and cos in the same loop for interesting patterns. Let's code it together!