Trigonometry Explained
Trigonometry isn't about triangles. It's about circles.
The triangle is just how the circle reveals itself when you freeze a moment of rotation. Sine, cosine, tangent — these aren't triangle measurements. They're coordinates of a point spinning around a center.
This changes everything about how trigonometry feels. Once you see the circle hiding inside every triangle, the subject transforms from memorizing ratios to understanding rotation.
What You'll Learn
This series covers the mathematics of circles hiding in triangles:
- What Is Trigonometry? — Why triangles are circles in disguise
- Sine Explained — The vertical position on a spinning circle
- Cosine Explained — The horizontal partner to sine
- Tangent Explained — The ratio that measures slope
- The Unit Circle — Why radius 1 changes everything
- SOH CAH TOA — The mnemonic that hides the meaning
- The Law of Sines — Every triangle inscribed in a circle
- The Law of Cosines — Pythagoras for any triangle
- Trigonometric Identities — Why sin²θ + cos²θ had to equal 1
- Radians vs Degrees — Why mathematicians prefer radians
- Waves and Oscillation — Why sine shows up everywhere
- Synthesis — Trigonometry as the language of cycles
The Core Insight
Trigonometry is the mathematics of circular motion frozen at a moment in time. Every sine value, every cosine, every tangent comes from a point on a circle.
When you learn trigonometry this way, you're not memorizing formulas. You're learning to see the rotation hiding in everything that oscillates, cycles, or repeats.
This is the hub page for the Trigonometry series.
Next: What Is Trigonometry? The Mathematics of Circles Hiding in Triangles
The Series
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