Powers, roots, logarithms, and trigonometric functions
Square Root: √x = number that, when multiplied by itself, equals x. Logarithms: log₁₀(x) finds the power to which 10 must be raised to get x; ln(x) uses base e (≈2.718). Trigonometry: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. Factorial: n! = n × (n-1) × (n-2) × ... × 1.
Scientific functions are fundamental in physics, engineering, finance, and advanced mathematics. Square roots appear in distance formulas and standard deviations. Logarithms model exponential growth and decibel scales. Trigonometry is essential for navigation, waves, and periodic phenomena. Factorials are used in probability and combinatorics.
This calculator uses degrees for trigonometric functions. A full circle is 360° or 2π radians. To convert: degrees × (π/180) = radians; radians × (180/π) = degrees. Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2. Most scientific and engineering applications use radians, while everyday measurements typically use degrees.
Remember that trigonometric functions are periodic—sin(θ) = sin(θ + 360°). Logarithms are only defined for positive numbers. Factorials grow extremely fast (13! exceeds 6 billion). For square roots of negative numbers, you enter complex number territory. Always check if your answer makes sense in context, and be aware of rounding errors in chained calculations.
Natural logarithm (ln) is the logarithm to base e (approximately 2.718). It's used extensively in calculus, physics, and engineering for continuous growth/decay calculations.
Our calculator uses degrees for trigonometric functions (sin, cos, tan). Enter the angle in degrees and the calculator converts to radians internally for the calculation.
Factorial (n!) is the product of all positive integers up to n. For example, 5! = 5×4×3×2×1 = 120. Factorials are used in combinatorics, probability, and algebra.