Trigonometry

Success Criteria

At the end of this chapter, students are able to:

  1. Find the trigonometric ratio of obtuse angles.

  2. Apply the trigonometric formula to find the area of a triangle.

  3. Apply the Sine Rule to find unknown sides and angles of a triangle.

  4. Apply the Cosine Rule to find unknown sides and angles of a triangle.

  5. Find the bearing of one point from another point.

  6. Find the angle of elevation and depression.

  7. Solve 3D-geometry problems using trigonometry (AO2).

Additionally, 3D/AR Applets for selected National Exam Questions can be found here.

Students can also choose to extend their knowledge through the following olympiad topics:

  1. Stewart's Theorem.

  2. Apollonius's Theorem.

  3. Parallelogram Law

Introduction to Trigonometry

Trigonometry is the study of triangles. It is a branch of mathematics that studies the relationship between the lengths and angles of a triangle.

Recap of Definitions

The hypotenuse (H) is defined as the longest side of the triangle and it is opposite the right-angle.

When we are taking the trigonometric ratio of a particular angle, we call that angle the reference angle (θ).

The adjacent (A) is the side that forms the reference angle together with the hypotenuse.

Lastly, the opposite (O) is the side that does not touch the reference angle.

The Trigonometric Ratios