Trigonometric Ratios in Right Triangles
Sine, Cosine, and Tangent — SAT Math Mastery
📐 Introduction: What is Trigonometry?
Trigonometry is the study of relationships between the sides and angles of triangles. The word comes from Greek: trigonon (triangle) + metron (measure).
At the heart of trigonometry are trigonometric ratios — ratios of sides in a right triangle. The three primary ratios are:
- sin Sine — ratio of opposite to hypotenuse
- cos Cosine — ratio of adjacent to hypotenuse
- tan Tangent — ratio of opposite to adjacent
Each ratio is a function of an angle, commonly represented by the Greek letter θ (theta). These ratios depend only on the angle — not on the size of the triangle.
🌍 Why does trigonometry matter? It's used in navigation, engineering, physics, architecture, computer graphics, astronomy, and much more. On the SAT, trig questions appear regularly and are very scoreable once you master the basics.
🔺 Right Triangle Basics
Key Vocabulary
| Right Triangle | A triangle with one 90° angle |
| Hypotenuse | The side opposite the right angle; always the longest side |
| Legs | The two sides that form the right angle |
| Reference Angle (θ) | The acute angle we use for trig ratios (NOT the 90° angle) |
| Opposite Side | The leg across from the reference angle |
| Adjacent Side | The leg next to the reference angle (not the hypotenuse) |
⚠️ Position matters! The "opposite" and "adjacent" sides change depending on which angle is the reference angle. Always identify your reference angle first!
Interactive visualization — available in the full lesson