Sum and difference identities

What You'll Learn

Apply sum and difference identities to evaluate sine, cosine, and tangent of angle combinations

Recognize how to break complex angles into sums or differences of special angles

Use Pythagorean identities to find missing trigonometric ratios from given values

Convert between radian and degree measures to simplify identity applications

Verify factored trigonometric expressions by applying sum and difference formulas

What You'll Practice

Simplifying expressions using sine and cosine sum and difference identities

Evaluating tangent of non-standard angles without a calculator

Proving trigonometric identities by expanding sum and difference formulas

Finding exact values by converting radians to degrees and applying special triangles

Determining trig ratios in different quadrants using reference angles

Why This Matters

Sum and difference identities are essential tools for solving complex trigonometric equations in calculus, physics, and engineering. You'll use these formulas to simplify expressions, prove identities, and evaluate exact valuesskills that appear in standardized tests and advanced STEM courses.

Before You Start — Make Sure You Can:

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )Trigonometric ratios of angles in radians

This Unit Includes

8 Video lessons

Practice exercises

Skills

Sum Identities

Difference Identities

Trigonometric Identities

Special Triangles

Reference Angles

Exact Values

Radian Conversion

Identity Proofs

OH Curriculum Aligned