Coterminal Angles
Angles differing by full turns share terminal side.
Key idea
Angles differing by full turns share terminal side.
In depth
Angles that end at the same terminal side differ by full turns: θ + 360°k. They have the same trig values, since the point on the unit circle is the same.
Worked example
Coterminal with 40°: 400°, −320°. So sin 400° = sin 40°.
Formula
Real-world uses
- Setting a robot arm or a wheel to an equivalent angle after many full turns
- Reading compass headings past 360°
Common mistake
Adding 180° instead of 360°.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Coterminal Angles?
Angles differing by full turns share terminal side. It is a topic at the intermediate level in Trigonometry.
What is the formula for Coterminal Angles?
The key formula is θ + 360°k.
Where is Coterminal Angles used in real life?
Real-world examples: Setting a robot arm or a wheel to an equivalent angle after many full turns; Reading compass headings past 360°.
What should I learn before Coterminal Angles?
Make sure you are comfortable with Quadrant Signs (ASTC), the previous topic in Trigonometry.
What is a common mistake with Coterminal Angles?
Adding 180° instead of 360°.
How can I practise Coterminal Angles?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Coterminal Angles?
Move on to Graph of Sine next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.