BEGINNER CONCEPTS

Triangle Properties

• Triangles are referenced by 3 letters. The triangle reference can start with any letter

(Ex: The triangle above can be referenced as Triangle…ABC, ACB, BAC, BCA, CBA, CAB, etc)

• The sides of triangles are typically referenced by lowercase letters (a, b, c) and corners are by uppercase letters (A, B, C)

Sum of Angles

• The sum of all angles in a triangle = 180° (angle A + angle B + angle C = 180°)

Right Triangle Properties

• Right triangles have one 90° angle, which is opposite of the hypotenuse

• A hypotenuse is only found in a right triangle

Ratio of Sides

• cos θ = adj / hyp = b/c

• sin θ = opp / hyp = a/c

• tan θ = opp / adj = a/b

• Acronym to remember formulas: sohcahtoa (sin opposite hypotenuse cos adjacent hypotenuse tan opposite adjacent)

• These properties are ratios, so the same equation can have multiple values (sin θ = 2/3 = 4/6 = 6/9)

ADVANCED CONCEPTS

Cosecant (CSC), Secant (SEC), Cotangent (COT)

• csc θ = 1 / sin θ

• sec θ = 1 / cos θ

• cot θ = 1 / tan θ

Know the following values to help solve problems

• sin 0° = 0 sin 30° = 1/2 sin 45° = √ 2 / 2 sin 60° = √ 3 / 2 sin 90° = 1

• cos 0° = 1 cos 30° = √ 3 / 2 cos 45° = √ 2 / 2 cos 60° = ½ cos 90° = 0

• tan 0° = 0 tan 30° = √ 3 / 3 tan 45° = 1 tan 60° = √ 3 tan 90° = undefined