Introduction
Trigonometry studies the relationships between the angles and sides of triangles, while coordinate geometry describes points, lines and shapes using number pairs on a plane. In BCS, bank and IT-officer written and MCQ exams these two topics appear together very often: a question may ask for the height of a tower from an angle of elevation, or the distance between two points, or the area of a triangle from its coordinates. Because every answer is a single number reached by a fixed method, these are among the most reliably scorable marks on the paper — if you know the formulas and the special-angle values cold, you rarely get them wrong.
This lesson builds both subjects from first principles, gives you the memory tables you must have, and walks through the exact problem types examiners repeat.
Learning objectives
- Define the six trigonometric ratios sin, cos, tan, cosec, sec, cot from a right triangle.
- Reproduce the special-angle table for 0°, 30°, 45°, 60°, 90° from memory.
- Apply the identities sin²θ + cos²θ = 1 and sec²θ − tan²θ = 1.
- Solve height-and-distance problems using angles of elevation and depression (poles, ladders, shadows, towers).
- Use the distance formula, midpoint, section formula, and centroid.
- Find the slope and equation of a line, and the perpendicular distance from a point or the origin to a line.
- Compute the distance between two parallel lines and the area of a triangle from coordinates.