Mathematics — Category Pages

Bearings, Heights and Distances

Trigonometry can recover a height or distance that is difficult to measure directly. A valid calculation requires a diagram that identifies where the observer stands, which line is…

Inverse Trigonometric Functions

Inverse trigonometric functions answer a reverse question: if a trigonometric ratio is known, which principal angle produces it? Arcsine, arccosine and arctangent are the most common examples. Because…

Inverse Trigonometric Identities

Inverse trigonometric identities combine familiar trigonometric relationships with the principal branches of arcsine, arccosine and arctangent. The algebra can look simple, but the branch conditions are part of…

Radians, Arc Length and Circular Motion

A wheel can make the same turn whether it is small or large, but a point on its rim travels farther on the larger wheel. Radian measure separates…

Sine Rule and Cosine Rule

A triangle does not need a right angle for its sides and angles to be related. The sine rule connects opposite side-angle pairs. The cosine rule connects three…

Sinusoidal Modelling

A sinusoidal model describes a quantity that rises and falls in a smooth repeating pattern. The model parameters describe the measured quantity’s maximum and minimum, timing and repetition.…

Polar Coordinates and Trigonometry

Cartesian coordinates locate a point by horizontal and vertical displacements. Polar coordinates locate it by a radius and a direction angle. They are especially useful when a problem…

Continuity of Functions

Continuity formalizes the idea that a function behaves without a break at a point or across an interval. Limits make that idea precise and separate removable holes from…

Limits in Calculus

Limits describe what a function approaches near a point or as inputs grow without bound. They let calculus reason about behaviour even when direct substitution fails, a graph…

Introduction to Differential Calculus

Differential calculus describes rates of change. It begins with average rates of change, then uses limits to describe an instantaneous rate. The result is the derivative: a quantity…

Calculus

Calculus studies change and accumulation through limits, derivatives and integrals. These lessons explain the assumptions behind each method and connect symbolic calculations with graphs and rates of change.…

Lines and Angles

An angle measures a turn between two directions. A line describes a straight path that continues indefinitely. Together, they let us describe corners, crossings, slopes and the shape…