Trigonometry Functions Explained — sin, cos, tan and Beyond
Trigonometric functions relate angles to the ratios of sides in a right triangle. sin θ is the ratio of the opposite side to the hypotenuse; cos θ is the ratio of the adjacent side to the hypotenuse; tan θ is opposite over adjacent. The three reciprocal functions — csc (cosecant), sec (secant), and cot (cotangent) — are simply the inverses of sin, cos, and tan respectively.
Key applications of trigonometry:
1. Architecture and construction — Roof pitch, slope gradients, and structural load calculations all rely on sin, cos, and tan.
2. Physics — Vector decomposition (forces, velocity), simple harmonic motion, and wave equations use trig functions as a foundation.
3. Navigation and surveying — Triangulation for GPS, land surveying, and celestial navigation all depend on trigonometric calculations.
4. Computer graphics — 2D and 3D rotation transforms, animation cycles, and procedural generation use sin and cos extensively.
5. Electrical engineering — Alternating current (AC) signals, waveform analysis, and signal processing are built on sine waves.
6. Astronomy — Calculating planetary orbits, distances, and angles uses trigonometry at every step.
Key values to remember: sin(30°) = 0.5, sin(45°) ≈ 0.7071, sin(60°) ≈ 0.8660, cos(90°) = 0, tan(45°) = 1. tan(90°) and cot(0°) are undefined because the denominator equals zero at those angles.
Frequently Asked Questions
A: Yes. Both decimals (35.5°) and negative angles (−30°) are fully supported.
A: Enter the numerical value instead of the symbol. For π/2 enter 1.5708, for π enter 3.14159.
A: Yes. The Pythagorean identity sin²θ + cos²θ = 1 holds for every angle. You can verify it using the results shown in the table.