Pythagorean identity and basic trig identities

What you'll learn

1. State the Pythagorean identity sin^2theta + cos^2theta = 1 and explain why it holds for any angle using the unit circle
2. Rearrange the Pythagorean identity to isolate sin^2theta or cos^2theta, and use the result to find one trig value given another and the quadrant
3. Derive tan^2theta + 1 = sec^2theta and 1 + cot^2theta = csc^2theta by dividing the Pythagorean identity by cos^2theta or sin^2theta
4. Apply quotient identities (tantheta = sintheta/costheta, cottheta = costheta/sintheta) 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)