Basics of Trigonometry Cheat Sheet

Key Definitions

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

• Angle: Measure of rotation between two rays. ✅

• Right Triangle: Triangle with one angle equal to 90°. ✅

• Hypotenuse: Longest side opposite the right angle. ✅

• Opposite Side: Side opposite to the angle of interest. ✅

• Adjacent Side: Side next to the angle of interest. ✅

Important Concepts

Trigonometric Ratios

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

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

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

Reciprocal Ratios

• Cosecant (csc): csc(θ) = 1/sin(θ) ✅

• Secant (sec): sec(θ) = 1/cos(θ) ✅

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

Key Formulas

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

• 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) ✅

Common Mistakes to Avoid

Common Mistake: Confusing sine and cosine ratios. Remember: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse.

Memory Tricks

Tip: "SOH-CAH-TOA" —

• Sine = Opposite / Hypotenuse

• Cosine = Adjacent / Hypotenuse

• Tangent = Opposite / Adjacent

Key Diagrams

         |\
         | \
    a    |  \  c
         |   \
         |____\
            b
Where:
c = Hypotenuse

a = Opposite side

b = Adjacent side