1. What is π radians in degrees?
- 180°
- 90°
- 360°
Check the answer and reasoning
180°
A full turn is 2π radians or 360°.
MATH / AS level
Radians and trigonometric identities
Radians measure angle through arc length divided by radius. Trigonometric graphs are periodic; transformations change amplitude, period or phase.
Learning objectives
- Explain radians and trigonometric identities using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Radians measure angle through arc length divided by radius. Trigonometric graphs are periodic; transformations change amplitude, period or phase.
Identities hold throughout their domain, while equations are true only at particular angles. Solve over the requested interval and retain all valid quadrants.
Equations and relationships
Arc length requires θ in radians.
Worked example
A circle of radius 4 m subtends 1.5 radians. Find arc length.
Follow the solution
Multiply radius by the radian angle: s = 4 × 1.5 = 6 m.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. A circle of radius 4 m subtends 1.5 radians. Find arc length.
- 2.67 m
- 6 m
- 6 m²
Check the answer and reasoning
6 m
Multiply radius by the radian angle: s = 4 × 1.5 = 6 m.
3. On 0° ≤ x ≤ 180°, sin x = 1/2 has which solutions?
- 30° only
- 30° and 210°
- 30° and 150°
Check the answer and reasoning
30° and 150°
Sine is positive in both first and second quadrants.