Trigonometry Cheat Sheet

Key Definitions

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

• Angle: Measured in degrees (°) or radians (rad).

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

• Cosine (cos): Ratio of adjacent side to hypotenuse.

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

Important Concepts

Right Triangle Relationships

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

• Reciprocal Functions:

• csc(θ) = 1/sin(θ)

• sec(θ) = 1/cos(θ)

• cot(θ) = 1/tan(θ)

Angle Sum and Difference

• sin(A ± B) = sinA cosB ± cosA sinB ✅

• cos(A ± B) = cosA cosB ∓ sinA sinB ✅

• tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB) ✅

Key Formulas

• Basic Ratios:

• sin(θ) = Opposite / Hypotenuse ✅

• cos(θ) = Adjacent / Hypotenuse ✅

• tan(θ) = Opposite / Adjacent ✅

• Area of Triangle:

• Law of Sines:

• Law of Cosines:

Common Mistakes to Avoid

Common Mistake: Confusing sine and cosine values for complementary angles (e.g., sin(90° - θ) = cos(θ)).

Memory Tricks

Tip: "SOH-CAH-TOA" —

• Sine = Opposite / Hypotenuse

• Cosine = Adjacent / Hypotenuse

• Tangent = Opposite / Adjacent

Key Diagrams

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

• In the triangle above:

• a: Opposite side

• b: Adjacent side

• c: Hypotenuse

Tip: Remember the unit circle for angle values and their sine/cosine results!