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Grade 11 Math Lab: Transcendence & Limits FREE
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Advanced Unit Circle & Trig Identities
Learning Objectives
- Master all quadrant values
- Apply Pythagorean identities
- Simplify expressions
Key Concepts
Pythagorean Identity
sin²θ + cos²θ = 1
ASTC Rule
All Students Take Calculus — signs by quadrant
Theory
**Pythagorean Identities:**
- sin²θ + cos²θ = 1
- tan²θ + 1 = sec²θ
- 1 + cot²θ = csc²θ
**Signs by quadrant (ASTC):**
- Q1: All positive
- Q2: Sin positive
- Q3: Tan positive
- Q4: Cos positive
**Reference angles:** Always measured to x-axis.
Examples
If sinθ = 3/5 in Q2, find cosθ
Solution: cos²θ = 1 - 9/25 = 16/25 → cosθ = -4/5 (negative in Q2)