Free online trigonometric calculator for all six functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Supports both degrees and radians. No registration required.
Practical Use Cases
Trigonometric calculators are essential across many fields:
1. Physics and Engineering
Wave analysis: y = A sin(ωt). Projectile motion: horizontal = v cos(θ), vertical = v sin(θ). Force components: Fx = F cos(θ), Fy = F sin(θ). AC circuits: voltage and current phase relationships. Essential for mechanics, optics, and electrical engineering.
2. Navigation and Surveying
Calculate distances and bearings: distance = d / sin(angle). Triangulation for GPS and mapping. Marine navigation: course corrections using bearings. Land surveying: measure inaccessible distances. Altitude and elevation calculations for aerial surveys.
3. Computer Graphics and Game Development
Rotation transformations: x' = x cos(θ) - y sin(θ). Camera movements and view angles. Object positioning in 3D space. Animation curves and circular motion. Lighting calculations: cos(θ) for light intensity falloff. Collision detection using angle calculations.
4. Architecture and Construction
Roof pitch calculations: tan(angle) = rise/run. Staircase design: sin(θ) for optimal step height. Solar panel angles for maximum efficiency. Structural load distribution. Bridge arc calculations. Building shadow analysis for sunlight planning.
5. Astronomy and Satellite Communications
Celestial object positions: altitude and azimuth using sin/cos. Satellite dish alignment angles. Orbital mechanics calculations. Eclipse predictions using angular relationships. Telescope pointing: convert celestial coordinates. Planet positions and visibility windows.
What are Trigonometric Functions?
Trigonometric functions relate angles to ratios of sides in right triangles. They are fundamental to mathematics, physics, engineering, and computer science.
The Six Trigonometric Functions
Basic functions: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent = sin/cos. Reciprocal functions: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ) = cos/sin. Each function has specific properties and applications in mathematics and science.
Degrees vs Radians
Degrees: Circle divided into 360 parts. Common angles: 0°, 30°, 45°, 60°, 90°, 180°. Radians: Angle measured in radius lengths. Full circle = 2π radians ≈ 6.28319. Conversion: degrees × π/180 = radians, radians × 180/π = degrees. Radians are natural units for calculus; degrees are intuitive for everyday use.
Common Angle Values
sin(0°)=0, sin(30°)=0.5, sin(45°)=√2/2≈0.707, sin(60°)=√3/2≈0.866, sin(90°)=1. cos(0°)=1, cos(30°)=√3/2≈0.866, cos(45°)=√2/2≈0.707, cos(60°)=0.5, cos(90°)=0. tan(0°)=0, tan(30°)=√3/3≈0.577, tan(45°)=1, tan(60°)=√3≈1.732, tan(90°)=undefined. These are fundamental values memorized in trigonometry.