Understanding Trigonometry
What Is Trigonometry?
Trigonometry studies the relationships between angles and sides of triangles. The six trigonometric functions — sin, cos, tan, cosec, sec, cot — define ratios between sides of a right triangle based on an angle.
The Six Trigonometric Functions
For angle θ in a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. The reciprocal functions are cosec = 1/sin, sec = 1/cos, cot = 1/tan.
Unit Circle
The unit circle has radius 1 centered at the origin. Any angle θ corresponds to a point (cos θ, sin θ) on the circle. This extends trig functions to all angles, not just acute angles in triangles.
Common Angle Values
sin 0° = 0, sin 30° = 0.5, sin 45° = √2/2, sin 60° = √3/2, sin 90° = 1. These exact values appear frequently and are worth memorizing.
Applications
Navigation, surveying, physics (wave motion, oscillations), engineering (force analysis, structural calculations), computer graphics (rotations, projections), and signal processing (Fourier transforms).