The Pythagorean Identity

sin² + cos² = 1

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\sin^2\theta + \cos^2\theta = 1$, from Pythagoras on the unit circle.
• Knowing one ratio (and the quadrant) gives the other.
• Dividing through gives $\tan^2\theta + 1 = \sec^2\theta$.

Steps

1. Around the circle
2. Find the cosine
3. In the second quadrant
4. Tangent from sine
5. Simplify
6. Another form