Trigonometry: Sine, Cosine and Tangent Ratios

Introduction

Trigonometry studies the relationship between the angles and sides of a right-angled triangle. The three sides are the hypotenuse (longest side, opposite the right angle), the opposite (facing the angle) and the adjacent (next to the angle).

The Three Basic Ratios

• Sine (sin): opposite / hypotenuse
• Cosine (cos): adjacent / hypotenuse
• Tangent (tan): opposite / adjacent

A common memory aid is SOH-CAH-TOA.

Worked Example

In a right triangle, if the opposite side = 3 and hypotenuse = 5, then sin(theta) = 3/5 = 0.6.

Angles of Elevation and Depression

The angle of elevation is measured upward from the horizontal to an object above; the angle of depression is measured downward to an object below. These appear often in height-and-distance word problems.

Special Angles

Learners should memorise sin, cos and tan values for 30°, 45° and 60°, as these appear often in exams.