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Pythagorean identities
What You'll Learn
Derive the three Pythagorean identities from the unit circle and Pythagorean theorem
Apply sine²θ + cos²θ = 1 to prove tan²θ + 1 = sec²θ and 1 + cot²θ = csc²θ
Recognize when to substitute Pythagorean identities in trigonometric expressions
Use quotient and reciprocal identities to convert between trig functions
Simplify complex expressions by combining fractions and applying conjugates
What You'll Practice
1
Proving Pythagorean identities using the unit circle definition
2
Simplifying expressions with sec²x - 1 and other Pythagorean forms
3
Combining trigonometric fractions with common denominators
4
Multiplying by conjugates to create difference of squares patterns
5
Verifying complex trigonometric identities step-by-step
Why This Matters
Pythagorean identities are essential tools you'll use throughout trigonometry, precalculus, and calculus. They allow you to simplify complex expressions, solve equations, and verify identitiesskills critical for understanding wave functions, circular motion, and advanced calculus techniques like integration.
This Unit Includes
5 Video lessons
Practice exercises
Learning resources
Skills
Pythagorean Identities
Unit Circle
Trigonometry
Identity Proofs
Algebraic Manipulation
Conjugates
Simplification
OH Curriculum Aligned