Geometry & Trigonometry

3D geometry studies the properties, measurements, and relationships of points, lines, planes, and solids in three-dimensional space. Learners will understand how to calculate volumes, surface areas, and spatial coordinates for engineering, computer graphics, and physics applications.

Analytic geometry uses algebraic equations to represent and analyze geometric shapes on a coordinate plane. Learners will understand how to define lines, curves, and conic sections mathematically, bridging the gap between algebra and visual geometry.

This topic covers the geometric properties, theorems, and equations of circles. Learners will understand how to calculate circumference, area, arc length, and sector area, as well as analyze relationships involving tangents, secants, and chords.

Coordinate geometry, or Cartesian geometry, studies geometric figures by placing them in a coordinate system. Learners will understand how to calculate distances, midpoints, slopes, and equations of lines, enabling the algebraic analysis of geometric shapes.

Euclidean geometry is the study of flat spaces, points, lines, and angles based on the axioms of Euclid. Learners will understand geometric proofs, congruence, similarity, and the fundamental theorems governing triangles, polygons, and circles.

Geometry and topology study the properties, shapes, and structures of spaces. Learners will understand geometric theorems, coordinate systems, and topological concepts like continuity, compactness, and properties preserved under continuous deformation.

The Law of Sines and the Law of Cosines relate the sides and angles of non-right triangles. Learners will understand how to solve for unknown distances and angles in oblique triangles, which is essential for navigation, surveying, and physics.

This field explores the properties of geometric shapes and spaces that are preserved under continuous deformations. Learners will understand concepts like continuity, compactness, manifolds, and the mathematical structure of spatial relationships.

This topic explores the properties, classifications, and theorems of triangles and multi-sided polygons. Learners will understand interior and exterior angles, perimeter, area, and congruence criteria, establishing a foundation for advanced geometric and trigonometric analysis.

Trigonometric functions relate the angles of a right triangle to ratios of its sides. Learners will understand sine, cosine, tangent, and their reciprocals, including how to graph these periodic functions and model real-world cyclical phenomena.

Trigonometric identities are mathematical equations involving trigonometric functions that hold true for all variables. Learners will understand how to simplify complex expressions, prove mathematical statements, and solve trigonometric equations using Pythagorean, sum, and double-angle formulas.

The unit circle is a circle of radius one centered at the origin, used to define trigonometric functions for all real numbers. Learners will understand how to find exact values of sine, cosine, and tangent using radian and degree measurements.