Trigonometry

Introduction to Trigonometry

Trigonometry studies relationships between angles and sides in triangles, particularly right triangles.

Right Triangle Basics

In a right triangle:

• Hypotenuse: The longest side opposite the right angle
• Opposite: Side opposite the angle of interest
• Adjacent: Side next to the angle of interest

Trigonometric Ratios (SOH-CAH-TOA)

Sine: sin(θ) = Opposite / Hypotenuse

Cosine: cos(θ) = Adjacent / Hypotenuse

Tangent: tan(θ) = Opposite / Adjacent

Pythagorean Theorem

a² + b² = c², where c is the hypotenuse

Example: If a = 3 and b = 4, then c = √(9 + 16) = √25 = 5

Special Angles

30°-60°-90° Triangle: Sides in ratio 1 : √3 : 2

45°-45°-90° Triangle: Sides in ratio 1 : 1 : √2

Angle Measures

• Degrees: 0° to 360°
• Radians: 0 to 2π, where π radians = 180°