Scientific Calculator

In a right triangle with angle θ:

sin(θ) = opposite side / hypotenuse

cos(θ) = adjacent side / hypotenuse

tan(θ) = opposite side / adjacent side

A helpful mnemonic: SOH-CAH-TOA (Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent=Opposite/Adjacent)

All three functions describe the relationships between angles and sides in triangles. They're fundamental in physics, engineering, and navigation.

log (Log₁₀): Common logarithm with base 10. Used in chemistry (pH scale), acoustics (decibels), earthquakes (Richter scale), and many engineering applications.

ln (Natural Logarithm): Logarithm with base e (≈2.718). Used in physics, biology (population growth), finance (continuous compounding), and calculus.

Key Difference: log(100) = 2 because 10² = 100. But ln(e) = 1 because e¹ = e.

In higher mathematics, natural log (ln) is more fundamental, but both are essential for different applications.

Degrees (0°-360°) are more intuitive for most people. Radians are the "natural" mathematical unit (used in calculus), but degrees are easier to visualize.

This calculator automatically converts your degree input to radians for the computation, then returns the result. It's more user-friendly!

Conversion Formula: radians = degrees × (π/180)

Examples: 90° = π/2 radians, 180° = π radians, 360° = 2π radians

π (pi) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's approximately 3.14159265...

Why is it important?

• Circumference of circle = 2πr

• Area of circle = πr²

• Volume of sphere = (4/3)πr³

π appears everywhere in mathematics, physics, and engineering. It's irrational (never-ending, non-repeating decimal) and has been studied for thousands of years.

No, not with real numbers. The square root of a negative number results in an imaginary number (involving i = √-1), which is beyond the scope of this calculator.

For example: √(-4) = 2i (not a real number)

In engineering and advanced physics, imaginary numbers are used, but this scientific calculator focuses on real number operations for accessibility.

If you try to calculate √ of a negative number, the calculator will show "Error".

Logarithms are undefined for zero and negative numbers in the real number system.

log(0) = undefined (mathematically, it approaches negative infinity)

log(negative) = undefined (no real solution)

If you attempt these operations, the calculator will display "Error". Always ensure your input is a positive number before using log or ln functions.

This is why logarithms work so well for measuring positive quantities like intensity, concentration, and growth rates.

This calculator uses standard JavaScript mathematical functions, which are accurate to approximately 15 significant digits for most operations.

For practical purposes, this precision is more than sufficient for:

• Engineering calculations

• Physics problems

• Academic work

• Financial calculations

However, for specialized fields requiring extreme precision (cryptography, scientific research), dedicated software like Mathematica or MATLAB would be more appropriate.