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Scientific Calculator: Trigonometry Logs & Engineering Guide

A scientific calculator performs advanced mathematical operations for engineering, physics, mathematics and chemistry problems. Trigonometric functions, logarithms, exponentials, factorial, combinations and permutations, all available in one interface.

📋 How to Use This Calculator

  1. Select mode, DEG (degrees) or RAD (radians) for trigonometry.
  2. Select a function, sin, cos, tan, log, ln, √, x², xⁿ, etc.
  3. Enter the value and press Enter/=.
  4. For inverse functions, use the 2nd/Shift button (sin⁻¹, cos⁻¹, etc.).

📐 Formula & Working Principle

Trigonometry: sin²θ + cos²θ = 1. tan θ = sin θ/cos θ.
Logarithms: log(ab) = log a + log b. ln(eˣ) = x.
Quadratic: x = [−b ± √(b²−4ac)] / 2a.
Factorial: n! = n×(n−1)×…×1.

💡 Worked Example

Structural engineering: Resolve a 100 N force at 30°.
Fx = 100×cos30° = 86.6 N. Fy = 100×sin30° = 50 N.
Physics: pH = −log[H⁺] = −log(0.001) = 3 (acidic).

❓ Frequently Asked Questions (FAQ)

Q: When should DEG vs RAD mode be used?

DEG (Degrees): geometry, navigation, everyday angles (0°–360°). RAD (Radians): calculus, physics formulas, programming math libraries. π radians = 180°.

Q: What is the difference between natural log (ln) and common log (log)?

ln = log base e (≈2.71828). log = log base 10. ln is used in calculus and exponential growth/decay formulas. log is used in decibels, pH and the Richter scale.

Q: How do you convert between polar and rectangular coordinates?

Polar (r, θ) → Rectangular (x, y): x = r×cos θ, y = r×sin θ. Rectangular → Polar: r = √(x²+y²), θ = tan⁻¹(y/x).

Q: How should significant figures be managed on a calculator?

The calculator displays maximum precision. In engineering, maintain the significant figures of your input data. Rule: the result should have no more significant figures than the least precise input.

Q: How are large factorials calculated?

Most calculators handle up to 69! exactly (70! overflows). Stirling's approximation: ln(n!) ≈ n×ln(n) − n + 0.5×ln(2πn).