Bearings and Navigation

Key idea

Compass angles used to solve distance problems.

In depth

A bearing is an angle measured clockwise from north, written with three digits. Combine bearings with the sine and cosine rules to find distances and directions in navigation problems.

Worked example

Sailing 10 km on bearing 060°: east component 10 sin 60° ≈ 8.66, north 10 cos 60° = 5.

Real-world uses

• Plotting flight paths, ship courses and hiking routes using compass bearings

Common mistake

Measuring from east or anticlockwise as in maths class.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Trigonometry

• Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
• Phase Shift – Horizontal translation of a wave.
• Vertical Shift and Midline – Moves the wave up or down.
• General Sinusoid – Combine amplitude, period, phase and shift.
• Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
• Pythagorean Identity – The key identity from the unit circle.