Lesson 6 of 12Article22 min
Trigonometry & the Unit Circle
Right-triangle ratios (SOH-CAH-TOA) extend to all angles via the unit circle: cos θ = x-coordinate, sin θ = y-coordinate of the point at angle θ from the positive x-axis.
From triangles to the circle
Right-triangle ratios (SOH-CAH-TOA) extend to all angles via the unit circle: cos θ = x-coordinate, sin θ = y-coordinate of the point at angle θ from the positive x-axis.
Key angles to memorise
- 0, π/6, π/4, π/3, π/2 and their quadrant cousins.
- sin(π/6)=1/2, sin(π/4)=√2/2, sin(π/3)=√3/2.
- cos mirrors sin with a π/2 shift: cos θ = sin(π/2 − θ).
- All Students Take Calculus — sign chart by quadrant.