Trigonometry Calculators
Free sin, cos, tan, Pythagorean theorem, and triangle solver calculators. All six trig ratios, degree and radian modes, law of sines and cosines.
Trigonometry Calculators - Angles, Ratios, and Triangle Solutions
Trigonometry is foundational in physics (vector decomposition, wave equations), engineering (structural analysis, signal processing), navigation, surveying, architecture, and computer graphics. These calculators handle every common trigonometric computation - from a simple sine lookup to a full triangle solution.
Three Trigonometry Calculators
Sin, Cos, Tan Calculator - All six trig ratios (sin, cos, tan, cosec, sec, cot) for any angle in degrees or radians. Also computes inverse functions (arcsin, arccos, arctan) - enter a ratio and find the corresponding angle. Shows the quadrant the angle falls in and the sign of each ratio (CAST rule). Special angle exact values shown (sin 30° = 1/2, cos 45° = √2/2, etc.).
Pythagorean Theorem Calculator - For right triangles: a² + b² = c². Enter any two sides and find the third, plus all vertex angles using inverse trig. Identifies Pythagorean triples (3-4-5, 5-12-13, 8-15-17). Use it with the Rectangle Calculator for diagonal verification, or the Beam Load Calculator for structural geometry.
Triangle Solver - Solves any triangle from any three known values: SSS, SAS, AAS, ASA, or SSA (ambiguous case detected and both solutions shown). Uses the law of sines (a/sin A = b/sin B) and law of cosines (c² = a² + b² − 2ab·cos C). Returns all missing sides, angles, area, and perimeter.
Trigonometry in the Real World
Construction - Roof pitch of 6:12 is an angle of arctan(6/12) = 26.6°. Stair riser-to-run ratios. The Pythagorean Theorem Calculator verifies square corners using the 3-4-5 check. Physics - Decompose force vectors: Fx = F·cos(θ), Fy = F·sin(θ) - see the Force Calculator for applied use. Surveying - The Triangle Solver handles bearing calculations and distance triangulation.
Frequently Asked Questions
What is the difference between sin⁻¹ and 1/sin?
sin⁻¹(x) (arcsin) is the inverse function - it takes a ratio and returns an angle. 1/sin(x) is cosecant (csc). They are completely different. arcsin(0.5) = 30°; csc(30°) = 1/sin(30°) = 2. Both are available in the Sin Cos Tan Calculator.
What is the ambiguous case in triangle solving?
When you know two sides and a non-included angle (SSA), there can be zero, one, or two valid triangles. The Triangle Solver detects this and, when two solutions exist, returns both triangles with their complete values.
When should I use the law of sines vs. law of cosines?
Law of sines (a/sin A = b/sin B) for AAS, ASA, or SSA. Law of cosines (c² = a² + b² − 2ab cos C) for SSS or SAS. The Triangle Solver applies the correct law automatically based on your inputs.
What are the exact values of sin, cos, tan for standard angles?
sin 0°=0, sin 30°=1/2, sin 45°=√2/2, sin 60°=√3/2, sin 90°=1. cos is the mirror image. tan 30°=1/√3, tan 45°=1, tan 60°=√3. The Sin Cos Tan Calculator shows exact forms for these special angles.