Scientific Calculator: Functions Beyond the Four Operations

Most people use calculators for basic arithmetic. The scientific functions come out infrequently enough that it's worth having a reference for what each one does.

Exponents and Roots

xⁿ or x^y: x raised to the power y. 2^10 = 1024.

√x: square root. √144 = 12.

ⁿ√x: nth root. ∛27 = 3 (cube root of 27).

eˣ: natural exponential. e ≈ 2.71828. e^1 = 2.71828.

Logarithms

log (log₁₀): common logarithm (base 10). log(1000) = 3 because 10³ = 1000.

ln: natural logarithm (base e). ln(e) = 1.

Relationship: ln(x) = log(x) / log(e) ≈ log(x) / 0.4343

Practical use: "How many digits does this number have?" digits ≈ floor(log₁₀(n)) + 1. The number 1,000,000 has 7 digits; log₁₀(1,000,000) = 6; floor(6) + 1 = 7. ✓

Trigonometry

sin, cos, tan: ratios in a right triangle. sin(θ) = opposite/hypotenuse. cos(θ) = adjacent/hypotenuse. tan(θ) = opposite/adjacent.

Inverse trig (sin⁻¹, cos⁻¹, tan⁻¹, also written arcsin, arccos, arctan): given a ratio, returns the angle.

Important: most calculators default to degrees mode. Scientific calculations in physics and calculus typically use radians. Check your mode.

Factorial (n!)

n! = n × (n-1) × (n-2) × ... × 2 × 1

5! = 5 × 4 × 3 × 2 × 1 = 120

Used in probability (permutations and combinations) and series expansions.

Large factorials get enormous fast: 20! ≈ 2.43 × 10¹⁸.

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