Trigonometry — The cosine rule

About this lesson

This unit focuses on the cosine rule for any triangle. It begins with a real-life problem involving two ships moving from a port in different directions, prompting students to find the distance between them. The text then derives the cosine rule using Pythagoras' theorem and the sine and cosine of an angle, presenting formulas for sides and angles. It explains how to use the cosine rule to find an unknown side when two sides and the included angle are known, and to find an angle when all three sides are known. The unit includes worked examples, activities with a scientific calculator, and applications to geometric shapes like quadrilaterals and parallelograms, as well as life problems such as navigation, agriculture, and architecture. By the end, students should be able to apply the cosine rule to solve triangles, find unknown sides and angles, and use it in various mathematical and practical contexts, including proving cyclic quadrilaterals and solving perimeter and area problems.