Pythagorean identity and basic trig identities

What you'll learn

1. State the Pythagorean identity sin²θ + cos²θ = 1 and explain why it holds for any angle using the unit circle
2. Rearrange the Pythagorean identity to isolate sin²θ or cos²θ, and use the result to find one trig value given another and the quadrant
3. Derive tan²θ + 1 = sec²θ and 1 + cot²θ = csc²θ by dividing the Pythagorean identity by cos²θ or sin²θ
4. Apply quotient identities (tanθ = sinθ/cosθ, cotθ = cosθ/sinθ) to convert between trig functions
5. Simplify trig expressions and solve ACT-style identity problems within 60 seconds

Prerequisites

• Trigonometric ratios (SOH-CAH-TOA)
• Unit circle values (key angles)