Exploring the World of Trigonometry

Trigonometric functions arise from the study of triangles, especially right triangles. The main functions are sine (\( \sin \)), cosine (\( \cos \)), and tangent (\( \tan \)). They relate the angles of a triangle to the lengths of its sides.

Unit Circle Connection

The unit circle (a circle with radius 1 centered at the origin) is a powerful tool for understanding trig functions. The \( x \)-coordinate corresponds to \( \cos(\theta) \), and the \( y \)-coordinate to \( \sin(\theta) \), where \( \theta \) is the angle from the positive \( x \)-axis.

Trig Function Properties

• Periodicity: They repeat in cycles.
• Amplitude: The height from the center to the peak.
• Applications: Used in physics, engineering, and music!

Real-Life Uses

Trigonometry helps us model sound waves, measure distances, and even understand the movement of planets.