Trigonometry Values and Memorization Techniques

Overview

• Explanation of how to remember trigonometry values using reference triangles.
• Creation of a table with sine, cosine, and tangent values at specific angles.
• Use of special right triangles (30-60-90 and 45-45-90) for calculating trigonometric functions.
• Introduction of the SOHCAHTOA mnemonic for sine, cosine, and tangent ratios.

Trigonometry Table Values

• Angles: 0°, 30° (π/6), 45° (π/4), 60° (π/3), 90° (π/2)
• Sine Values:
  • 0°: 0
  • 30°: 1/2
  • 45°: √2/2
  • 60°: √3/2
  • 90°: 1
• Cosine Values:
  • Reverse order of sine values, 0°: 1 to 90°: 0
• Tangent Values:
  • Calculated as sine divided by cosine
  • 0°: 0
  • 30°: √3/3
  • 45°: 1
  • 60°: √3
  • 90°: Undefined

Reference Triangles

30-60-90 Triangle

• Side Lengths: Across 30° is 1, across 90° is 2, across 60° is √3
• Using SOHCAHTOA:
  • Sine 30°: Opposite/Hypotenuse = 1/2
  • Cosine 30°: Adjacent/Hypotenuse = √3/2
  • Tangent 30°: Opposite/Adjacent, rationalize to √3/3
  • Tangent 60°: Opposite/Adjacent = √3
  • Sine 60°: Opposite/Hypotenuse = √3/2

45-45-90 Triangle

• Side Lengths: Both legs are 1, hypotenuse is √2
• Using SOHCAHTOA:
  • Sine 45°: Opposite/Hypotenuse, rationalize to √2/2
  • Cosine 45°: Same as sine 45° = √2/2
  • Tangent 45°: Opposite/Adjacent = 1

Reciprocal Functions

• Secant (sec): Reciprocal of cosine
  • sec 60° = 1/cos 60° = 2
• Cosecant (csc): Reciprocal of sine
  • csc 60° = 1/sin 60°, rationalize to 2√3/3
• Cotangent (cot): Reciprocal of tangent
  • cot 60° = 1/tan 60°, rationalize to √3/3

Conclusion

• Explanation of the usefulness of these triangles and methods in evaluating trigonometric functions.
• Encouragement to subscribe, like, and comment on the video.