MathIsimple

Trigonometric Identities

Master fundamental trigonometric identities, sum and difference formulas, double-angle identities, and learn to simplify and transform trigonometric expressions.

11th Grade
Trigonometry
~60 min
🎮 Interactive Activity: Identity Verifier

Verify if the trigonometric identity is true!

Identity:

sin²θ + cos²θ = 1
🎮 Interactive Activity: Identity Transformer

Simplify using trigonometric identities!

Expression:

sin²θ + cos²θ
1. Basic Pythagorean Identities

Fundamental Pythagorean Identities

The three main Pythagorean identities are:

  • sin²θ + cos²θ = 1
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = csc²θ
Example 1: Verify Identity

Problem: Show that sin²(30°) + cos²(30°) = 1

Step 1: sin(30°) = 1/2, cos(30°) = √3/2

Step 2: sin²(30°) + cos²(30°) = (1/2)² + (√3/2)²

Step 3: = 1/4 + 3/4 = 4/4 = 1 ✓

Answer: Identity verified

Example 2: Simplify Expression

Problem: Simplify: 1 - cos²θ

Step 1: From sin²θ + cos²θ = 1, we get sin²θ = 1 - cos²θ

Answer: 1 - cos²θ = sin²θ

2. Sum and Difference Formulas
3. Double-Angle Formulas
4. Half-Angle Formulas
5. Product-to-Sum Identities
6. Sum-to-Product Identities
7. Proving Identities
8. Applications
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
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