10 questions🇬🇧English
🍕 Radians, Arcs & Sectors – A-level
Maths · A-level — radian conversions, arc length, sector and segment area, plus small-angle approximations
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Questions
What is 60° in radians?
π/3
π/6
π/4
2π/3
20s
What is 3π/4 radians in degrees?
270°
135°
150°
120°
20s
What is the exact value of sin(π/6)?
√2/2
√3/2
1
½
20s
A sector has radius 6 cm and angle 2π/3 radians. What is its arc length?
6π cm
4π cm
2π cm
12π cm
30s
A sector has radius 4 cm and angle π/4 radians. What is its area?
8π cm²
π cm²
2π cm²
4π cm²
30s
A sector of radius 5 cm has an arc length of 8 cm. What is the angle at the centre?
40 radians
0.625 radians
3.2 radians
1.6 radians
30s
A sector has radius 10 cm and angle 0.8 radians. What is its perimeter?
8 cm
28 cm
40 cm
18 cm
30s
A chord cuts off a segment of a circle of radius 6 cm, with angle π/3 at the centre. What is the segment's exact area?
(12π − 9√3) cm²
(6π − 9√3) cm²
(6π − 9) cm²
(3π − 9√3/2) cm²
60s
Using small-angle approximations, which expression approximates cos 2θ when θ is small?
1 − 4θ²
1 − 2θ²
1 − θ²/2
1 − θ²
30s
For small θ, what is the approximate value of (sin 3θ × tan θ) ÷ (1 − cos θ)?
6
9
3
3/2
60s