Trigonometric Ratios and Definitions

The Six Fundamental Relationships in Right Triangles

"Trigonometry - From Greek 'trigonon' (triangle) and 'metron' (measure) - The mathematics of measuring triangles and periodic phenomena"
Welcome to the fascinating world of trigonometric ratios! Let's discover how simple triangles unlock the secrets of circles, waves, and periodic motion.
📐 Right Triangle Foundation

All trigonometric ratios are based on right triangles. The three sides relative to any acute angle are: opposite (across from the angle), adjacent (next to the angle), and hypotenuse (longest side).

Right Triangle = Foundation
90° angle + two acute angles
📊 Primary Ratios (SOH-CAH-TOA)

The three primary trigonometric ratios relate the sides of a right triangle to its angles. These form the foundation for all trigonometric calculations.

sin θ = Opp/Hyp, cos θ = Adj/Hyp, tan θ = Opp/Adj
Remember: SOH-CAH-TOA
🔄 Reciprocal Ratios

Each primary ratio has a reciprocal: cosecant (1/sine), secant (1/cosine), and cotangent (1/tangent). These provide alternative ways to express relationships.

csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
Reciprocals expand our toolkit
🔗 Fundamental Identity

The quotient relationship connects sine and cosine to tangent, providing a bridge between the ratios and enabling complex calculations.

tan θ = sin θ / cos θ
The bridge between ratios