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📐 Scientific Calculator Formulas

Trigonometry (RAD mode)

sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent = sin/cos

sin²(θ) + cos²(θ) = 1 (Pythagorean identity)

DEG → RAD: radians = degrees × π/180
RAD → DEG: degrees = radians × 180/π

Logarithms

log(x) = log base 10 of x (common log)
ln(x) = log base e of x (natural log)
log₂(x) = log base 2 of x (binary log)

log(a×b) = log(a) + log(b)
log(a/b) = log(a) − log(b)
log(aⁿ) = n × log(a)

Change of base: logₙ(x) = ln(x) / ln(n)

Powers & Roots

x² = x × x
x³ = x × x × x
xⁿ = x raised to power n
√x = square root of x = x^(1/2)
∛x = cube root of x = x^(1/3)

eˣ = Euler's number (2.718...) to power x
10ˣ = 10 raised to power x

Factorial

n! = n × (n−1) × (n−2) × ... × 2 × 1

0! = 1 (by definition)
1! = 1
5! = 5×4×3×2×1 = 120
10! = 3,628,800

Mathematical Constants

π (Pi) = 3.14159265358979...
e (Euler) = 2.71828182845904...
φ (Phi) = 1.61803398874989... (Golden Ratio)

φ = (1 + √5) / 2
e = lim(n→∞) (1 + 1/n)ⁿ

Scientific Notation

Standard form: a × 10ⁿ where 1 ≤ a < 10

Examples:
5,000,000 = 5 × 10⁶ = 5E+6
0.000042 = 4.2 × 10⁻⁵ = 4.2E-5
Speed of light: 3 × 10⁸ m/s

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