Understanding the Unit Circle

Introduction

• The unit circle is a fundamental concept in trigonometry.
• It is a circle with a radius of one, centered at the origin of the coordinate plane.

Key Features

• The circle represents angles in both radians and degrees.
• Important angles include 0°, 30°, 45°, 60°, 90°, etc., up to 360°.
• Each angle has corresponding coordinates on the circle.

Trigonometric Functions

• Sine (sin): Value of y-coordinate at a given angle.
• Cosine (cos): Value of x-coordinate at a given angle.
• Tangent (tan): Ratio of sine to cosine (y/x).

Quadrants

• Divided into four quadrants:
  1. Quadrant I: 0° to 90°
  2. Quadrant II: 90° to 180°
  3. Quadrant III: 180° to 270°
  4. Quadrant IV: 270° to 360°
• Each quadrant affects the sign of the trigonometric functions.

Special Angles and Their Coordinates

• 30° (π/6): (√3/2, 1/2)
• 45° (π/4): (√2/2, √2/2)
• 60° (π/3): (1/2, √3/2)

Application

• Useful in solving trigonometric equations.
• Helps in understanding periodic functions and waveforms.

Visualization

• Always refer to the unit circle when solving trigonometry problems for a visual understanding of angles and their sine, cosine, and tangent values.