Trigonometry Study Guide

Trigonometry is the study of the relationship between the sides and angles of triangles. In the JAMB syllabus, this covers basic ratios, angles of elevation and depression, bearings, and graph analysis.

1. Trigonometrical Ratios

For a right-angled triangle, the primary ratios are:

• Sine (sin): Opposite / Hypotenuse
• Cosine (cos): Adjacent / Hypotenuse
• Tangent (tan): Opposite / Adjacent

Use the mnemonic SOH CAH TOA to remember these.

2. Angles in the Four Quadrants (CAST Rule)

Angles can range from -360° to 360°. The sign of the ratio depends on the quadrant:

• 1st Quadrant (0-90°): All ratios are positive.
• 2nd Quadrant (90-180°): Only Sine is positive. (sin θ = sin(180 - θ))
• 3rd Quadrant (180-270°): Only Tangent is positive. (tan θ = tan(θ - 180))
• 4th Quadrant (270-360°): Only Cosine is positive. (cos θ = cos(360 - θ))

3. Special Angles

Common values to memorize:

• 30°: sin 30 = 1/2, cos 30 = √3/2, tan 30 = 1/√3
• 45°: sin 45 = 1/√2, cos 45 = 1/√2, tan 45 = 1
• 60°: sin 60 = √3/2, cos 60 = 1/2, tan 60 = √3

4. Elevation and Depression

Angle of Elevation: The angle between the horizontal line and the line of sight when looking up at an object.

Angle of Depression: The angle between the horizontal line and the line of sight when looking down at an object. Note: The angle of elevation from object A to B is equal to the angle of depression from B to A.

5. Bearings

Bearings measure direction clockwise from the North line (000°). They are always written in three digits (e.g., 045°).

6. Sine and Cosine Formulae

• Sine Rule: a/sin A = b/sin B = c/sin C. Used when two angles and one side or two sides and a non-included angle are given.
• Cosine Rule: a² = b² + c² - 2bc cos A. Used when two sides and an included angle or three sides are given.
• Area of Triangle: Area = ½ ab sin C.

7. Graphs of Sine and Cosine

The graph of y = sin x starts at 0, peaks at (90, 1), crosses 0 at 180, and reaches -1 at 270. The graph of y = cos x starts at (0, 1), crosses 0 at 90, and reaches -1 at 180.