Interactive Scientific Calculator

Trigonometric functions relate the angles of a triangle to the ratios of its sides. The three primary functions are:

• sin(θ): Opposite / Hypotenuse — used in wave analysis, alternating current, and pendulum problems
• cos(θ): Adjacent / Hypotenuse — used in vector decomposition and force calculations
• tan(θ): Opposite / Adjacent — used in slope calculations and navigation

The inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) allow you to find an angle when you know the ratio. For example, sin⁻¹(0.5) = 30°. Make sure to check whether you're in RAD or DEG mode — sin(30) in RAD mode gives −0.988, while in DEG mode it gives 0.5.

log is the common logarithm (base 10). It answers: "10 raised to what power gives me this number?" For example, log(100) = 2 because 10² = 100. It's used in the Richter scale (earthquakes), decibels (sound), and pH (chemistry).

ln is the natural logarithm (base e ≈ 2.71828). It answers: "e raised to what power gives me this number?" For example, ln(e) = 1 and ln(e²) = 2. It's fundamental in calculus, compound interest, radioactive decay, and population growth models.

Key relationship: ln(x) = log(x) × ln(10) ≈ log(x) × 2.3026

The yˣ function raises a base number (y) to an arbitrary exponent (x). Enter the base first, press yˣ, then enter the exponent and press =.

Examples:

• 2 yˣ 5 = 32 (2⁵ = 2 × 2 × 2 × 2 × 2)
• 9 yˣ 0.5 = 3 (square root of 9)
• 2 yˣ −1 = 0.5 (negative exponent = reciprocal)
• 4 yˣ 0.25 = √2 ≈ 1.414 (fourth root)

This is different from x² (square) and x³ (cube) which are one-tap shortcuts for common powers. Use yˣ for any custom exponent.

Factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in permutations, combinations, and probability calculations.

Key values:

• 0! = 1 (by definition)
• 1! = 1
• 5! = 120
• 10! = 3,628,800
• 20! ≈ 2.43 × 10¹⁸

Limitations: This calculator supports factorials up to 170! (which is approximately 7.26 × 10³⁰⁶). Values above 170! exceed the floating-point range. Factorials are only defined for non-negative integers — entering a decimal or negative number will produce an error.

Degrees divide a circle into 360 equal parts. Use degrees when working with geometry, architecture, navigation, and everyday angle measurements. A right angle is 90°.

Radians measure angles based on the arc length relative to the radius. One full circle = 2π radians ≈ 6.283. Use radians in calculus, physics, engineering, and any formula involving π (e.g., wave equations, angular velocity).

Conversion: radians = degrees × π / 180. So 90° = π/2 ≈ 1.5708 radians. Most programming languages and calculators use radians by default. This calculator defaults to RAD mode — tap the DEG button to switch.

Common mistake: sin(90) in RAD mode ≠ 1. You'll get 0.8940 instead. Always check your mode before computing trigonometric functions.