Trigonometry Cheat Sheet

Key Definitions

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

• Sine (sin): sin(θ) = Opposite/Hypotenuse ✅

• Cosine (cos): cos(θ) = Adjacent/Hypotenuse ✅

• Tangent (tan): tan(θ) = Opposite/Adjacent ✅

• Cosecant (csc): csc(θ) = 1/sin(θ) ✅

• Secant (sec): sec(θ) = 1/cos(θ) ✅

• Cotangent (cot): cot(θ) = 1/tan(θ) ✅

Important Concepts

Trigonometric Identities

• Pythagorean Identity: sin²(θ) + cos²(θ) = 1 ✅

• Angle Sum/Difference:

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

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

Inverse Trigonometric Functions

• sin⁻¹(x), cos⁻¹(x), tan⁻¹(x): Returns the angle whose trigonometric ratio is x. ✅

Key Formulas

• Area of Triangle: Area = 1/2 base height ✅

• Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) ✅

• Law of Cosines: c² = a² + b² - 2ab * cos(C) ✅

Common Mistakes to Avoid

Common Mistake: Forgetting to use radians in trigonometric functions when required.

Memory Tricks

Tip: "SOH-CAH-TOA" —

• Sine = Opposite / Hypotenuse

• Cosine = Adjacent / Hypotenuse

• Tangent = Opposite / Adjacent

Key Diagrams

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