Scientific Calculator

Operators: + − * / ^ (exponent), % (modulo), and parentheses for grouping. Multiplication is always explicit — write 2*pi, not 2pi.

Functions take exactly one argument in parentheses: sin, cos, tan, asin, acos, atan, ln (natural log), log (base-10), sqrt, abs, exp.

Constants: pi (π ≈ 3.14159…) and e (Euler's number ≈ 2.71828…). Numbers may use scientific notation, e.g. 1.5e3 = 1500.

Order of operations follows PEMDAS / BODMAS: parentheses, exponents, multiplication/division (left to right), addition/subtraction (left to right). Use parentheses generously — they cost nothing and prevent ambiguity.

The angle-mode toggle controls how trig functions interpret their input and output. In degree mode, sin(90) returns 1; in radian mode you would need sin(pi/2) to get the same result. Inverse trig (asin, acos, atan) follows the same convention — output is degrees in degree mode, radians in radian mode.

Calculus, physics, and most programming languages default to radians because the derivative formulas only work cleanly in radians — d/dx sin(x) = cos(x) only if x is measured in radians. Engineering, navigation, and everyday geometry usually use degrees. If a problem gives you angles in degrees and the answer looks suspiciously wrong, the first thing to check is the mode switch.

Compound interest: 1000 * (1 + 0.05) ^ 10 returns 1628.89 — the value of $1,000 invested for 10 years at 5% annual compounding.

Distance between two points: sqrt((4 − 1)^2 + (8 − 2)^2) returns 6.708, the straight-line distance from (1, 2) to (4, 8).

Solving for an unknown exponent: ln(2) / ln(1.07) returns 10.24 — the rule-of-72 confirmation that money invested at 7% doubles in about 10.24 years.

Trig in surveying: a 30-foot ladder leaning at 75° reaches up the wall 30 * sin(75) ≈ 28.98 feet (in degree mode) and stands 30 * cos(75) ≈ 7.76 feet from the base. Flip the mode toggle and the same expressions return wildly different numbers — a fast way to confirm the mode setting matches your input units.

'Invalid number' usually means a typo — two decimal points in a row, a stray letter, or scientific notation written without the e (write 1.5e3, not 1.5 × 10^3).

'Unexpected character' is the parser's catch-all for syntax it does not recognize: a smart-quote pasted from a word processor, an em-dash where a minus sign was intended, or a Greek π character. Replace with straight ASCII punctuation and the word 'pi'.

Division by zero returns Infinity, not an error — the JavaScript number type uses IEEE 754, which represents 1/0 as positive infinity. Multiplying that by anything finite still gives infinity; multiplying it by zero gives NaN ('not a number').

asin(2) returns NaN because the sine of a real angle is always between -1 and 1, so the inverse sine is only defined on that range. The same applies to acos. atan accepts any real input.

Floating-point rounding shows up most often in trig: cos(90) in degree mode returns about 6 × 10⁻¹⁷, not exactly zero, because π/2 cannot be represented exactly in binary. For symbolic exactness, use a CAS (Wolfram Alpha, SymPy). For engineering accuracy, the floating-point result is the correct answer.