Trigonometry
Master trigonometric ratios, special angles, identities, equations, and graphs
Trigonometry is the study of relationships between angles and sides in triangles. This topic covers the fundamental concepts you'll need for Grade 10 and beyond, including trigonometric ratios, special angles, identities, equations, and graphs.
Learning Outcomes
- Define and use sine, cosine, and tangent ratios
- Recall trigonometric values for special angles (0°, 30°, 45°, 60°, 90°)
- Apply the quotient identity (tan θ = sin θ / cos θ)
- Apply the Pythagorean identity (sin²θ + cos²θ = 1)
- Solve basic trigonometric equations
- Sketch and interpret sine, cosine, and tangent graphs
Topic Sections
Trigonometric Ratios
Learn SOH CAH TOA, identify opposite, adjacent, and hypotenuse sides, find unknown sides and angles
ExploreSpecial Angles
Memorize sin, cos, tan values for 0°, 30°, 45°, 60°, 90° using geometric derivations
ExploreTrigonometric Identities
Understand and apply the quotient identity and Pythagorean identity to simplify expressions
ExploreTrigonometric Equations
Solve equations of the form sin θ = k, cos θ = k, and tan θ = k using reference angles
ExploreTrigonometric Graphs
Sketch and interpret sine, cosine, and tangent graphs with transformations
ExploreQuick Reference
SOH CAH TOA
Pythagorean Identity
Quotient Identity
Special Angles
Quick Check: What do you know?
Test your understanding of trigonometry before diving into the topics.
Hint: Remember the Pythagorean identity - it's one of the most important!
Key Terms
Study Tips for Trigonometry
- Memorize SOH CAH TOA - it's the foundation for all trigonometric ratios
- Learn the special angle values (0°, 30°, 45°, 60°, 90°) - they appear in many problems
- Practice using the Pythagorean identity sin²θ + cos²θ = 1
- Always draw a diagram when solving right triangle problems
- Use the interactive games and quizzes in each topic to test your understanding
