Memorizing the Unit Circle

Introduction

• Focus on memorizing the Unit Circle and its components.
• Importance of understanding angles in radians.

Angles in Radians

• 0 degrees = 0 radians.
• Full Circle = 2π radians.
• Half Circle = π radians.
• Quarter Circle = π/2 radians.
• Breakdown:
  • 1π/4, 2π/4 (π/2), 3π/4, 4π/4 (π)
  • 5π/4, 6π/4 (3π/2), 7π/4, 8π/4 (2π)

Angles in Parts

• Divide the circle into 8 equal parts.
• Additional angles:
  • 1π/6, 2π/6 (π/3), 3π/6 (π/2)
  • 4π/6 (2π/3), 5π/6, 6π/6 (π)
  • 7π/6, 8π/6 (4π/3), 9π/6 (3π/2)
  • 10π/6 (5π/3), 11π/6

Values on Axes

• X-axis: Right (x=1), Left (x=-1)
• Y-axis: Top (y=1), Bottom (y=-1), Center (x=0, y=0)

Quadrants

1. Quadrant I: x and y positive.
2. Quadrant II: x negative, y positive.
3. Quadrant III: x and y negative.
4. Quadrant IV: x positive, y negative.

Values for Key Angles

• Quadrant I (increase x from 0 to 1):
  • x: 1/2, √2/2, √3/2, 1
  • y: 0, √1/2, √2/2, √3/2, 1
• Quadrant II: Reflect values of Quadrant I, x is negative.
• Quadrant III: Both x and y negative.
• Quadrant IV: x positive, y negative.

Converting Radian to Degrees

• π = 180 degrees.
• Conversion:
  • π/6 = 30°
  • π/4 = 45°
  • π/3 = 60°
  • π/2 = 90°
  • 2π/3 = 120°
  • 3π/4 = 135°
  • 5π/6 = 150°
  • π = 180°
  • 7π/6 = 210°
  • 5π/4 = 225°
  • 4π/3 = 240°
  • 3π/2 = 270°
  • 5π/3 = 300°
  • 7π/4 = 315°
  • 11π/6 = 330°

Using the Unit Circle for Trig Functions

• Sine: Use y-value.
  • Example: sine(π/3) = √3/2
• Cosine: Use x-value.
  • Example: cosine(7π/6) = -√3/2
• Tangent: y/x or sine/cosine.
  • Example: tan(π/3) = √3

Conclusion

• Recap of the techniques to memorize and utilize the unit circle.
• Encouragement to comment, like, and subscribe for more content.