Scientific Calculator
How do you use sin, cos, tan, log, and ln on a scientific calculator?
Type mathematical expressions directly or use the function buttons to insert operations. The calculator supports standard arithmetic (+, -, *, /), trigonometric functions (sin, cos, tan and their inverses), logarithms (log for base-10, ln for natural log), square roots, powers (using ^), absolute values, factorials, and the constants PI and e. — also see our exponent calculator. — also see our square root calculator. — also see our fraction calculator. See also: the Log Calculator and the Exponent Calculator.
Trigonometric Functions
All trigonometric functions in this calculator use degrees (not radians). sin(90) returns 1, cos(0) returns 1, and tan(45) returns 1. Inverse functions (asin, acos, atan) also return results in degrees. For radians, multiply degrees by PI/180.
Order of Operations
The calculator follows standard mathematical order of operations (PEMDAS/BODMAS): Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). Use parentheses to control the order of evaluation when needed.
Tips for Complex Expressions
You can combine multiple operations in a single expression. For example, "sin(45)*2 + sqrt(16)" calculates the sine of 45 degrees multiplied by 2, plus the square root of 16. Use parentheses to group operations and ensure correct evaluation order.
How does scientific calculator: practical work?
The Scientific Calculator is built for people who want a fast answer without losing context. It keeps the calculation simple, shows the result clearly, and helps you understand what the number means before you use it in a real decision.
This calculator is designed to make a specific everyday calculation faster and clearer. It gives a structured result so you can compare options, check assumptions, or plan the next step with less manual work.
When to use a scientific calculator
A scientific calculator extends beyond basic arithmetic (+, –, ×, ÷) to support advanced mathematical functions needed in higher education, science, engineering, and finance. The key capabilities that distinguish a scientific calculator from a basic calculator include trigonometric functions, logarithms, exponents, roots, factorial calculations, and support for scientific notation.
What is trigonometric functions?
Trigonometric functions relate angles to ratios of sides in right triangles. They are fundamental in physics, engineering, architecture, and navigation.
- sin(θ): Opposite ÷ Hypotenuse
- cos(θ): Adjacent ÷ Hypotenuse
- tan(θ): Opposite ÷ Adjacent = sin(θ) ÷ cos(θ)
Important values to memorise:
- sin(0°) = 0 | sin(30°) = 0.5 | sin(45°) ≈ 0.707 | sin(60°) ≈ 0.866 | sin(90°) = 1
- cos(0°) = 1 | cos(30°) ≈ 0.866 | cos(45°) ≈ 0.707 | cos(60°) = 0.5 | cos(90°) = 0
- tan(45°) = 1 | tan(0°) = 0 | tan(90°) = undefined (infinity)
Degrees vs radians: Ensure your calculator is in the correct mode. Degrees: a full circle = 360°. Radians: a full circle = 2π ≈ 6.283. To convert: degrees × (π/180) = radians. Radians × (180/π) = degrees.
Logarithms
A logarithm answers the question "what exponent do we need to raise the base to, to get this number?"
- log₁₀(x): Base-10 logarithm (common log). log₁₀(1000) = 3 because 10³ = 1000
- ln(x): Natural logarithm (base e ≈ 2.71828). ln(e) = 1. ln(1) = 0.
- log₂(x): Base-2 logarithm, used in computer science. log₂(8) = 3 because 2³ = 8
Logarithm rules: log(A × B) = log(A) + log(B). log(A ÷ B) = log(A) – log(B). log(A^n) = n × log(A)
Factorials
The factorial of a non-negative integer n (written n!) is the product of all positive integers from 1 to n.
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 10! = 3,628,800
- 0! = 1 (by definition)
Factorials appear in permutations (n! = number of ways to arrange n items), combinations C(n,r) = n! ÷ (r! × (n–r)!), and probability calculations.
Order of operations (BODMAS/PEMDAS)
Mathematical operations must be performed in a specific order: Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction
Example: 3 + 4 × 2² – (6 ÷ 3)
Step 1 (Brackets): 6 ÷ 3 = 2. Expression: 3 + 4 × 4 – 2
Step 2 (Orders): 2² = 4. Expression: 3 + 4 × 4 – 2
Step 3 (Multiplication): 4 × 4 = 16. Expression: 3 + 16 – 2
Step 4 (Addition/Subtraction left to right): 3 + 16 – 2 = 17
For matrix operations (addition, multiplication, determinant), use the matrix calculator.
Order of operations (BODMAS/PEMDAS): common mistakes
BODMAS: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction. Common errors: 8 ÷ 2(2+2) = ? Many calculators give 16 (left-to-right division first: 8÷2=4, then 4×4=16). Some give 1 (treating 2(2+2) as 2×4=8 first, then 8÷8=1). The ambiguity exists because juxtaposition (implicit multiplication) is interpreted differently. To avoid: always use explicit parentheses: (8÷2)×(2+2) = 16 or 8÷(2×(2+2)) = 1. Modern scientific calculators follow strict left-to-right for division and multiplication.
Scientific notation: entering and reading on a calculator
Scientific notation expresses large/small numbers as a × 10ⁿ. Avogadro's number: 6.022 × 10²³ — enter as 6.022 EXP 23 (using the EXP or ×10ˣ button, not multiplying by 10). Speed of light: 3 × 10⁸ m/s. Electron charge: 1.602 × 10⁻¹⁹ C. Common errors: confusing EXP button with e (Euler's number). 6.022E23 means 6.022 × 10²³; e^23 means Euler's number raised to power 23 = 9.74 × 10⁹ — completely different values.
Frequently asked questions about scientific calculators
What is Euler's number (e)? e ≈ 2.71828 is a mathematical constant that is the base of the natural logarithm. It appears naturally in compound interest (continuous compounding), population growth, radioactive decay, and many physics equations. It is defined as the limit of (1 + 1/n)^n as n approaches infinity.
What is π (pi)? π ≈ 3.14159265 is the ratio of a circle's circumference to its diameter. It is an irrational number (cannot be expressed as a fraction of integers) and a transcendental number (not a root of any polynomial with rational coefficients). It appears in all calculations involving circles, spheres, and periodic phenomena.
How do I calculate combinations and permutations? Permutations (ordered arrangements): P(n,r) = n! ÷ (n–r)!. Combinations (unordered selections): C(n,r) = n! ÷ [r! × (n–r)!]. Example: How many 3-person committees from 8 people? C(8,3) = 8! ÷ (3! × 5!) = 56. — see also: log calculator — see also: quadratic formula calculator
Scientific calculator function reference
| Function | Symbol | Example | Result |
|---|---|---|---|
| Sine | sin | sin(30°) | 0.5 |
| Cosine | cos | cos(60°) | 0.5 |
| Tangent | tan | tan(45°) | 1 |
| Common logarithm | log | log(100) | 2 |
| Natural logarithm | ln | ln(e) | 1 |
| Square root | √ | √144 | 12 |
| Power | xⁿ | 2^10 | 1,024 |
| Factorial | n! | 5! | 120 |
| Pi | π | π × r² | 3.14159… |
| Euler's number | e | e^1 | 2.71828… |
Common trig values — quick reference
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 0.5 | √3/2 ≈ 0.866 | 1/√3 ≈ 0.577 |
| 45° | √2/2 ≈ 0.707 | √2/2 ≈ 0.707 | 1 |
| 60° | √3/2 ≈ 0.866 | 0.5 | √3 ≈ 1.732 |
| 90° | 1 | 0 | undefined |
| 180° | 0 | −1 | 0 |
Sources & References
Sources: NIST Digital Library of Mathematical Functions; IEEE 754 Standard for Floating-Point Arithmetic; Abramowitz, M. & Stegun, I. Handbook of Mathematical Functions, NIST.