MathIsimple

Advanced Trigonometry

Master trigonometric identities, special angles, double angle formulas, sum and difference identities, and apply trigonometry to solve complex problems!

10th Grade
Trigonometry
~60 min
🎮 Interactive Activity: Identity Verifier

Complete the trigonometric identity!

Identity:

sin²θ + cos²θ = ?
🎮 Interactive Activity: Angle Calculator

Find the exact value of the trigonometric function!

Problem:

Find sin(30°)
1. Introduction to Advanced Trigonometry

Beyond Right Triangles

Advanced trigonometry extends beyond right triangles to include identities, special angles, and formulas that simplify complex trigonometric expressions.

Key Topics:

  • Trigonometric identities (Pythagorean, reciprocal, quotient)
  • Special angle values (30°, 45°, 60°, 90°)
  • Double angle formulas
  • Sum and difference formulas
  • Unit circle concepts
Example 1: Using Identities

Simplify: sin²θ + cos²θ

Solution: By the Pythagorean identity, sin²θ + cos²θ = 1

Note: This is true for all values of θ

Example 2: Special Angles

Find sin(30°) and cos(60°)

sin(30°): In a 30-60-90 triangle, sin(30°) = opposite/hypotenuse = 1/2

cos(60°): In the same triangle, cos(60°) = adjacent/hypotenuse = 1/2

Note: sin(30°) = cos(60°) due to cofunction identity

2. Trigonometric Identities
3. Special Angles
4. Double Angle Formulas
5. Sum and Difference Formulas
6. Unit Circle Concepts
7. Real-World Applications
8. Problem-Solving Strategies
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is the Pythagorean identity?
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2
What is sin(30°)?
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3
What is cos(60°)?
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4
What is the double angle formula for sin(2θ)?
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5
Which identity is derived from sin²θ + cos²θ = 1?
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6
What is tan(45°)?
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7
What is sin(90° - θ) equal to?
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8
What is the period of y = sin(2x)?
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9
What is cos(180° - θ)?
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10
If sinθ = 3/5 and θ is in Q1, what is cosθ?
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