DEG vs RAD — The Most Common Mistake
The single most common scientific calculator mistake is using the wrong angle mode. Before solving any trigonometry problem, always verify your calculator is in the correct mode.
| Mode | Full Circle | When to Use | sin(90) = ? |
|---|---|---|---|
| DEG (Degrees) | 360° | Everyday geometry, engineering drawings, navigation | 1 ✅ |
| RAD (Radians) | 2π ≈ 6.283 | Calculus, advanced physics, programming | 0.894 ❌ (if you meant 90°) |
| GRAD (Gradians) | 400 grad | Surveying — rarely used in schools | Varies |
Conversion: Degrees to Radians = degrees × π/180. Radians to Degrees = radians × 180/π.
Trigonometric Functions — sin, cos, tan
These three functions relate angles to ratios of sides in a right triangle:
- sin(θ) = Opposite ÷ Hypotenuse
- cos(θ) = Adjacent ÷ Hypotenuse
- tan(θ) = Opposite ÷ Adjacent = sin(θ) ÷ cos(θ)
Key Values to Memorise (DEG mode)
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 0.5 | 0.866 | 0.577 |
| 45° | 0.707 | 0.707 | 1 |
| 60° | 0.866 | 0.5 | 1.732 |
| 90° | 1 | 0 | Undefined (∞) |
Inverse Trig Functions (sin⁻¹, cos⁻¹, tan⁻¹)
Inverse functions find the angle when you know the ratio. Press INV then sin/cos/tan:
- sin⁻¹(0.5) = 30° (in DEG mode)
- cos⁻¹(0.707) ≈ 45°
- tan⁻¹(1) = 45°
Logarithms — log and ln
Logarithms are the inverse of exponential functions:
- log (log₁₀) = common logarithm. log(100) = 2 (because 10² = 100)
- ln = natural logarithm (base e = 2.718). ln(e) = 1, ln(1) = 0
- 10ˣ (INV + log) = antilog. 10ˣ(2) = 100
- eˣ (INV + ln) = natural antilog. e¹ = 2.718
Change of base formula: log₂(8) = log(8) ÷ log(2) = 0.903 ÷ 0.301 = 3. Use this to calculate any logarithm base using log or ln buttons.
Powers and Roots
| Button | Function | Example | Result |
|---|---|---|---|
| x² | Square | 7² | 49 |
| x³ | Cube | 4³ | 64 |
| xⁿ | Any power | 2⁸ | 256 |
| √ | Square root | √169 | 13 |
| ∛ | Cube root | ∛27 | 3 |
| 1/x | Reciprocal | 1/8 | 0.125 |
Factorial (n!)
Factorial of n = product of all positive integers from 1 to n. 5! = 5×4×3×2×1 = 120.
Used in: permutations (nPr = n! ÷ (n-r)!), combinations (nCr = n! ÷ (r! × (n-r)!)), probability, and series expansions.
Note: 0! = 1 (by definition). Calculators can handle up to about 170! — beyond that, the number exceeds floating-point capacity.
π (Pi) and e (Euler's Number)
- π = 3.14159265... — ratio of circle circumference to diameter. Used in geometry, trigonometry, statistics.
- e = 2.71828182... — Euler's number, base of natural logarithm. Used in compound interest, population growth, radioactive decay.
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Open Scientific Calculator →Frequently Asked Questions
Q: Why does my scientific calculator give a different answer for sin(90)?
This almost always means your calculator is in RAD mode instead of DEG mode. sin(90°) = 1 in DEG mode. sin(90 radians) ≈ 0.894. Always check your mode before starting trig calculations. On most calculators, look for "DEG", "RAD", or "D/R" indicator on the display.
Q: How to calculate log base 2 on a scientific calculator?
Use the change of base formula: log₂(x) = log(x) ÷ log(2). Example: log₂(64) = log(64) ÷ log(2) = 1.806 ÷ 0.301 = 6. Alternatively: log₂(x) = ln(x) ÷ ln(2). Both give the same result.