What is an Algorithm? Definition, Examples

What is Area? Definition, Formula, Examples

Area is the size of a two-dimensional surface — how much space a flat shape occupies. It is measured in *square units* (m², cm², ft², in²). The most-used area formulas are: square ($A = a^2$), rectangle ($A = l \times w$), triangle ($A = \tfrac{1}{2} \times b \times h$), and circle ($A = \pi r^2$).

What is a Percent? Definition, Formula, Examples

percent (symbol: %) is a way to express a number as a fraction of 100. Percent means "per hundred" — so 25% means 25 out of 100, or $\tfrac{25}{100} = 0.25$. The formula to convert a fraction to a percentage is $\frac{\text{part}}{\text{whole}} \times 100$.

Radian - Definition, Formula, Conversion

A radian is the angle subtended at the centre of a circle by an arc whose length equals the radius. By definition, $\theta = s/r$ (arc length over radius). A full circle is $2\pi$ radians, so $360° = 2\pi$ rad, $180° = \pi$ rad, and $1\text{ rad} \approx 57.296°$.

Cos2x - Formula, Identity, Examples, Proof

The **cos2x identity** is the double-angle formula for cosine, with three equivalent forms: $$\cos 2x = \cos^2 x - \sin^2 x = 2\cos^2 x - 1 = 1 - 2\sin^2 x$$ The proof from the angle-sum identity, when to use each form, the related $\cos 2x$ in terms of $\tan x$, worked examples, and the most common student mistakes.

Trigonometry Formulas - Full list

The complete list of **trigonometry formulas** covers seven categories: basic ratios (sin, cos, tan), reciprocal identities (csc, sec, cot), Pythagorean identities ($\sin^2 + \cos^2 = 1$), angle-sum and angle-difference formulas, double-angle formulas, half-angle formulas, and sum-to-product formulas.

Sin Cos Tan - Trigonometric Ratios and Formulas