← Back to Module 2
1. The Unit Circle
Unit Circle: x² + y² = 1, center (0,0), radius 1.
cos θ = x-coordinate, sin θ = y-coordinate of point on unit circle at angle θ.
2. Quadrantal Angles
| θ | (cos, sin) |
|---|
| 0 | (1, 0) |
| π/2 | (0, 1) |
| π | (−1, 0) |
| 3π/2 | (0, −1) |
3. Special Angle Values (First Quadrant)
| θ | sin | cos | tan |
|---|
| π/6 (30°) | 1/2 | √3/2 | √3/3 |
| π/4 (45°) | √2/2 | √2/2 | 1 |
| π/3 (60°) | √3/2 | 1/2 | √3 |
4. Signs by Quadrant (ASTC)
QI: All +, QII: Sin +, QIII: Tan +, QIV: Cos +
5. Reference Angles
QI: θ' = θ | QII: θ' = π − θ | QIII: θ' = θ − π | QIV: θ' = 2π − θ
6. Pythagorean Identity
sin²θ + cos²θ = 1
7. Right Triangle Trig (SOH-CAH-TOA)
sin = Opp/Hyp cos = Adj/Hyp tan = Opp/Adj
csc = Hyp/Opp sec = Hyp/Adj cot = Adj/Opp
8. Cofunction Identities
sin θ = cos(90° − θ) tan θ = cot(90° − θ) sec θ = csc(90° − θ)
9. Applications
Angle of Elevation: up from horizontal. Angle of Depression: down from horizontal.
Strategy: Draw a diagram, label known/unknown sides and angles, choose the trig ratio that connects them.