Radians, degrees and arc length: Class 11 practice
π radians = 180°. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
The idea behind radians, degrees and arc length
π radians = 180°. To convert degrees to radians multiply by π/180; radians to degrees multiply by 180/π. Arc length l = rθ with θ in radians.
Step-by-step method
- Write the conversion factor.
- Multiply and simplify the fraction of π.
- For arcs, use l = rθ (θ in radians).
Worked example 1 (Basic)
Convert 135° to radians.
- 135 × π/180 = 3π/4
- Answer: 3π/4
Worked example 2 (Standard)
Convert 7π/6 radians to degrees.
- × 180/π
- = 210°
- Answer: 210°
Worked example 3 (Challenge)
Find the arc length of a circle of radius 10 cm cut off by a central angle of 75°. Leave π in the answer.
- θ = 5π/12
- l = rθ = 25/6π cm
- Answer: 25/6π cm
Common mistakes and misconceptions
- Using degrees in l = rθ
- Inverting the factor
Practice questions
- (Basic) Convert 120° to radians.
- (Basic) Convert 150° to radians.
- (Standard) Convert 5π/6 radians to degrees.
- (Standard) Convert π/12 radians to degrees.
- (Challenge) Find the arc length of a circle of radius 19 cm cut off by a central angle of 150°. Leave π in the answer.
- (Challenge) Find the arc length of a circle of radius 6 cm cut off by a central angle of 40°. Leave π in the answer.
Answer key with full working
- Q1: 120 × π/180 = 2π/3 → Answer: 2π/3
- Q2: 150 × π/180 = 5π/6 → Answer: 5π/6
- Q3: × 180/π → = 150° → Answer: 150°
- Q4: × 180/π → = 15° → Answer: 15°
- Q5: θ = 5π/6 → l = rθ = 95/6π cm → Answer: 95/6π cm
- Q6: θ = 2π/9 → l = rθ = 4/3π cm → Answer: 4/3π cm
Syllabus note
This skill is listed under "Trigonometric Functions" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is radians, degrees and arc length in?
"Trigonometric Functions", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.