CHSL Trigonometry Cheat Sheet

Key Definitions

• Trigonometry: Study of relationships between angles and sides of triangles.

• Angle: Formed by two rays with a common endpoint, measured in degrees (°) or radians (rad).

• Sine (sin): Ratio of the opposite side to the hypotenuse in a right triangle. ✅

• Cosine (cos): Ratio of the adjacent side to the hypotenuse in a right triangle. ✅

• Tangent (tan): Ratio of the opposite side to the adjacent side. ✅

Important Concepts

Right Triangle Relationships

• Pythagorean Theorem: a² + b² = c² where c is the hypotenuse. ✅

• SOH-CAH-TOA:

• SOH: sin(θ) = opposite/hypotenuse

• CAH: cos(θ) = adjacent/hypotenuse

• TOA: tan(θ) = opposite/adjacent

Unit Circle

• Coordinates: (cos(θ), sin(θ)) for angles in standard position.

• Key Angles: 0°, 30°, 45°, 60°, 90° with corresponding values.

Key Formulas

• sin²(θ) + cos²(θ) = 1 ✅

• tan(θ) = sin(θ)/cos(θ) ✅

• sin(2θ) = 2sin(θ)cos(θ) ✅

• cos(2θ) = cos²(θ) - sin²(θ) ✅

• tan(2θ) = 2tan(θ)/(1 - tan²(θ)) ✅

Common Mistakes to Avoid

Common Mistake: Confusing sin and cos values for specific angles (e.g., sin(60°) vs. cos(30°)).

Memory Tricks

Tip: "SOHCAHTOA" —

• S: Sine = Opposite/Hypotenuse

• C: Cosine = Adjacent/Hypotenuse

• T: Tangent = Opposite/Adjacent

Key Diagrams

      |\
      | \
  b   |  \ c
      |   \
      |____\
        a

• a: Adjacent side

• b: Opposite side

• c: Hypotenuse

Unit Circle:
        |
    (0,1) 
        |
(-1,0)---(1,0)
        |
    (0,-1)

• Key angles on the unit circle correspond to sin and cos values.