Trigonometric Ratios Explorer
About This MicroSim
This interactive visualization demonstrates the three basic trigonometric ratios in a right triangle:
- Sine (sin) - Red: Opposite / Hypotenuse
- Cosine (cos) - Blue: Adjacent / Hypotenuse
- Tangent (tan) - Purple: Opposite / Adjacent
Use the slider to change the angle θ and watch how all the ratios update in real-time.
SOH-CAH-TOA
The memory aid SOH-CAH-TOA helps you remember which sides to use:
| Ratio | Mnemonic | Formula |
|---|---|---|
| Sine | SOH | Sin = Opposite / Hypotenuse |
| Cosine | CAH | Cos = Adjacent / Hypotenuse |
| Tangent | TOA | Tan = Opposite / Adjacent |
Key Observations
As you change the angle θ:
- sin(θ) increases from near 0 to near 1 as θ goes from 0° to 90°
- cos(θ) decreases from near 1 to near 0 as θ goes from 0° to 90°
- tan(θ) increases without bound as θ approaches 90°
Special Angles
Try these common angles:
| Angle | sin | cos | tan |
|---|---|---|---|
| 30° | 0.5 | 0.866 | 0.577 |
| 45° | 0.707 | 0.707 | 1.0 |
| 60° | 0.866 | 0.5 | 1.732 |
Learning Objectives
- Identify opposite, adjacent, and hypotenuse relative to an angle
- Calculate sine, cosine, and tangent ratios
- Understand how trig ratios change as angles change
Bloom's Taxonomy Level
Understanding and Applying