In a circle of radius (r) the central angle is (150^\circ). What is the ratio of arc length to radius?
Answer and explanation
Correct answer: \(\frac{5\pi}{6}\)
The arc-length formula is \(s=r\theta\), where \(\theta\) must be measured in radians. Hence, \(\frac{s}{r}=\theta\). Since \(150^\circ=150\times\frac{\pi}{180}=\frac{5\pi}{6}\), the required ratio is \(\frac{5\pi}{6}\). Note that \(\frac{2\pi}{3}\) corresponds to \(120^\circ\), not \(150^\circ\). Exam tip: In arc-length questions, convert the angle to radians first.
Frequently asked questions
What is the correct answer to this question?
\(\frac{5\pi}{6}\)
Why is this the correct answer?
The arc-length formula is \(s=r\theta\), where \(\theta\) must be measured in radians. Hence, \(\frac{s}{r}=\theta\). Since \(150^\circ=150\times\frac{\pi}{180}=\frac{5\pi}{6}\), the required ratio is \(\frac{5\pi}{6}\). Note that \(\frac{2\pi}{3}\) corresponds to \(120^\circ\), not \(150^\circ\). Exam tip: In arc-length questions, convert the angle to radians first.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
