Right-Angled Triangles (Copy)

Cheat Sheet: Trigonometry in Right-Angled Triangles (IGCSE Mathematics 0580 – CORE)
Topic: Sine, Cosine, Tangent, and Solving 2D Problems

1. Basic Trigonometric Ratios

In a right-angled triangle:

2. Definitions

• Opposite: Side opposite to the given angle θ.
• Adjacent: Side next to the given angle θ (but not the hypotenuse).
• Hypotenuse: The longest side (opposite the right angle).

3. Finding a Side

• If given an angle and one side, use the correct ratio and rearrange:
  • To find opposite: opposite = hypotenuse × sin θ
  • To find adjacent: adjacent = hypotenuse × cos θ
  • To find opposite (using tan): opposite = adjacent × tan θ

4. Finding an Angle

• To find an angle when two sides are known:
  • sin θ = opposite ÷ hypotenuse → θ = sin⁻¹(opposite ÷ hypotenuse)
  • cos θ = adjacent ÷ hypotenuse → θ = cos⁻¹(adjacent ÷ hypotenuse)
  • tan θ = opposite ÷ adjacent → θ = tan⁻¹(opposite ÷ adjacent)

5. Important Points

• Make sure your calculator is set to DEGREES mode.
• Always give angles to 1 decimal place unless otherwise stated.
• Label sides carefully before choosing the correct formula.

6. Solving Problems in 2D

• Use Pythagoras’ theorem if no angle is given and you know two sides.
• Use trigonometry (sin, cos, tan) if an angle and one side are given or required.
• Problems may involve:
  • Triangles in real-life situations.
  • Bearings (measure clockwise from north).

7. Bearings

• Bearings are measured clockwise from North (000° to 360°).
• If needed, use trigonometry to find missing distances or angles, then apply bearing rules.

8. Quick Reference

This cheat sheet covers all CORE-level knowledge for using sine, cosine, and tangent in solving right-angled triangle problems and 2D trigonometric problems.