Sexagesimal System and Angle Measurements

This section explains the sexagesimal system for measuring angles and how to convert between different angle representations.

Key concepts:

• Incomplete and complete units in the sexagesimal system
• Converting between degrees, minutes, and seconds
• Adding and subtracting angles in sexagesimal form
• Handling angles greater than 360°

Example: To convert 32.75° to the sexagesimal system: 32° + (0.75 × 60') = 32° 45'

Definition: Sexagesimal system - An angle measurement system based on 60, using degrees, minutes, and seconds.

The page also demonstrates how to perform arithmetic operations with complex angle measurements and deal with angles exceeding 360°.

Fundamental Trigonometric Relationships

This section presents the core trigonometric identities and demonstrates their proofs.

Key relationships covered:

1. sin^2 x + cos^2 x = 1
2. tan x = sin x / cos x
3. 1 + tan^2 x = 1 / cos^2 x

Definition: Trigonometric identity - An equation involving trigonometric functions that is true for all values of the variables.

Example: Proof of sin^2 x + cos^2 x = 1 using the Pythagorean theorem in a right triangle.

The page also includes a table of trigonometric ratios for common angles (0°, 30°, 45°, 60°, 90°), which is essential for solving many trigonometry problems.