Trigonometry Cheat Sheet

Key Definitions

• Trigonometric Ratios: Ratios of the sides of a right triangle.

• Sine (sin): Opposite side / Hypotenuse

• Cosine (cos): Adjacent side / Hypotenuse

• Tangent (tan): Opposite side / Adjacent side

Important Concepts

Unit Circle

• Angles: Measured in degrees or radians (360° = 2π radians).

• Coordinates: On the unit circle, (cos θ, sin θ).

Pythagorean Identity

• sin² θ + cos² θ = 1 ✅

Key Formulas

• Basic Ratios:

• sin θ = Opposite / Hypotenuse

• cos θ = Adjacent / Hypotenuse

• tan θ = sin θ / cos θ

• Reciprocal Ratios:

• csc θ = 1/sin θ

• sec θ = 1/cos θ

• cot θ = 1/tan θ

• Angle Sum/Difference:

• sin(a ± b) = sin a cos b ± cos a sin b

• cos(a ± b) = cos a cos b ∓ sin a sin b

• Double Angle Formulas:

• sin(2θ) = 2sin θ cos θ

• cos(2θ) = cos² θ - sin² θ

Common Mistakes to Avoid

Common Mistake: Forgetting to convert angles to radians when using calculators.

Memory Tricks

Tip: "SOH-CAH-TOA" —

• Sine = Opposite / Hypotenuse

• Cosine = Adjacent / Hypotenuse

• Tangent = Opposite / Adjacent

Key Diagrams

      |\
      | \
  Opposite |  \ Hypotenuse
      |   \
      |____\
       Adjacent

Tip: Use the unit circle for quick reference to values of sin and cos for common angles (0°, 30°, 45°, 60°, 90°).