Scientific Calculator

When you calculate the sine, cosine, or tangent of an angle, the calculator needs to know how you are measuring that angle. There are two common systems: degrees and radians.

Degrees are the familiar everyday system. A full circle is 360 degrees. A right angle is 90 degrees. Most people learn angles in degrees first, so if you are doing basic geometry or navigation, use DEG mode.

Radians are the system preferred in advanced mathematics, physics, and programming. Instead of splitting a circle into 360 parts, radians measure angles by the arc length on a unit circle (a circle with radius 1). A full circle equals 2π radians (roughly 6.283). A right angle equals π/2 radians (roughly 1.5708). The conversion formula is: radians = degrees x (π / 180).

Why does it matter? If you type sin(90) in DEG mode, you get 1 (correct for a right angle). If you type sin(90) in RAD mode, you get approximately 0.894 - because 90 radians is a wildly large angle. Always confirm which mode you are in before computing trig values. This calculator prominently displays the current mode (DEG or RAD) at the top of the display.

Memory functions let you temporarily store a number so you can reuse it across multiple calculations without retyping it. This is especially useful in multi-step problems such as tax calculations, engineering formulas, or any situation where one intermediate result feeds into several later computations.

• M+ (Memory Add): Adds the number currently shown on the display to whatever is already in memory. If memory holds 10 and you press M+ while the display shows 5, memory becomes 15.
• M- (Memory Subtract): Subtracts the displayed number from memory. If memory holds 15 and you press M- while displaying 3, memory becomes 12.
• MR (Memory Recall): Pastes the stored number from memory onto the display, so you can use it in your current calculation.
• MC (Memory Clear): Resets memory to zero and removes the M indicator from the display.

A small orange M badge appears at the top right of the display whenever a non-zero value is stored in memory, reminding you that memory is active. Pressing MC clears memory and removes the indicator.

Both log and ln are logarithmic functions - they answer the question "what exponent do I need to raise a base to in order to get this number?" - but they use different bases.

Log (base 10), written log(x), asks: "10 to what power equals x?" For example, log(100) = 2 because 10² = 100. log(1000) = 3 because 10³ = 1000. Base-10 logarithms are heavily used in science for expressing very large or very small numbers (pH scales, decibels, earthquake magnitudes, and the Richter scale are all base-10 log scales).

Ln (Natural Logarithm), written ln(x), uses e (Euler's number, approximately 2.71828) as its base. It asks: "e to what power equals x?" For example, ln(e) = 1 and ln(1) = 0. Natural logs appear everywhere in calculus, compound interest formulas, radioactive decay, and population growth models because they naturally describe continuous exponential processes.

The two are related by the formula: ln(x) = log(x) / log(e), or equivalently log(x) = ln(x) / ln(10). For everyday unit conversions, base-10 is often more intuitive. For continuous growth or decay problems, natural log is the right choice.

When a mathematical expression contains multiple operations, the order in which you perform them dramatically changes the result. PEMDAS is the standard rule set that ensures everyone - and every calculator - arrives at the same answer. PEMDAS stands for:

• P - Parentheses: Evaluate expressions inside parentheses first.
• E - Exponents: Evaluate powers and roots next.
• M/D - Multiplication and Division: Performed left to right before addition or subtraction.
• A/S - Addition and Subtraction: Performed last, left to right.

Consider: 2 + 3 x 4. If you simply go left to right, you get (2+3) x 4 = 20. But PEMDAS says multiply first: 2 + (3x4) = 2 + 12 = 14. The correct answer is 14. This calculator strictly follows PEMDAS, parsing the full equation string before evaluating.

This is why the parenthesis buttons ( ) are so powerful. Typing (2 + 3) x 4 forces the addition to happen first, yielding 20. Use parentheses liberally to make your intent explicit, especially in multi-step financial or scientific calculations.

Trigonometric functions (trig functions) describe the relationship between angles and side lengths in right triangles. They are foundational in geometry, physics, engineering, architecture, music theory, and computer graphics.

Imagine a right triangle. Label one acute angle as theta. The three sides are: the side opposite theta, the side adjacent (next) to theta, and the hypotenuse (the longest side, always opposite the right angle). Then:

• sin(theta) = opposite / hypotenuse. Useful for finding heights from angles.
• cos(theta) = adjacent / hypotenuse. Useful for finding horizontal distances.
• tan(theta) = opposite / adjacent. Useful for finding slopes and gradients.

The inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) work in reverse - they take a ratio and give you back the angle. For example, if you know the opposite side is 5 and the hypotenuse is 10, then the angle is sin⁻¹(5/10) = sin⁻¹(0.5) = 30 degrees.

Real-world uses include: GPS navigation, calculating roof pitch angles in construction, wave analysis in audio engineering, and rendering 3D graphics on screens. Every time your phone knows which direction you are facing, trig is involved.