π Mathematics
Unit circle and trigonometry
See sin, cos and tan change as the angle turns.
Unit circle and trigonometry
💬 Questions and answers
1What am I looking at?
Answer: A circle of radius 1 with a turning radius, and the sine graph beside it.
2What are its parts? (click a part to identify it)
Answer: Angle θ, the point (cos θ, sin θ), the cos line (blue), sin line (red) and tan line (green).
3How does it work?
Answer: As the radius turns, its horizontal shadow is cos θ and its vertical height is sin θ; tan θ = sin θ ÷ cos θ.
4Why is it important?
Answer: Trigonometry is used for heights and distances, waves, engineering and navigation.
5What happens if I change something? (use the sliders)
Answer: Turn the angle or press play to see the sine wave being drawn.
6What should I remember for the exam?
Answer: sin²θ + cos²θ = 1. Signs by quadrant: All, Sin, Tan, Cos (I to IV). sin 30° = ½, cos 60° = ½, tan 45° = 1.