Exploring Triangles

Trigonometry is the study of relationships between angles and sides in triangles, especially right triangles.

Key Ratios

The three main trigonometric ratios are:

• Sine (\( \sin \))
• Cosine (\( \cos \))
• Tangent (\( \tan \))

For a right triangle:

• \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)
• \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
• \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

Applications

• Measuring heights and distances indirectly.
• Navigation and construction.
• Understanding waves and periodic phenomena.