Measuring angles with the circle itself

Mathematics · Geometry · ages 16-17

Name ______________________ Date ____________

What is 60 degrees in radians?
- pi over 6
- pi over 4
- pi over 3
A circle has radius 8 m. An arc subtends an angle of 0.25 radians at the centre. What is the arc length in metres?
Answer: ______________
What is 45 degrees in radians?
- pi/6
- pi/3
- pi/4
- pi/2
What is a full turn in radians?
- pi
- 2 pi
- pi over 2
Arc length equals r theta with theta in degrees.
Circle one: True False
What is the area of a sector of radius 6 cm and angle pi over 3?
- 12 pi square cm
- 6 pi square cm
- 2 pi square cm
A sector has radius 6 m and central angle 2 radians. What is its area in square metres?
Answer: ______________
A circle has radius 4 and angle 2 radians. What is the arc length?
Answer: ______________
An answer claims a sector area bigger than pi r squared. What do you know?
- It must be wrong, since a slice cannot beat the circle
- It must be right, since sectors run large
- Nothing, since sizes vary freely
Cosine of pi over 3 equals sine of which benchmark angle?
- pi over 4
- pi over 3
- pi over 6

Answer key

For grown-ups. Fold this page away before handing over the rest.

pi over 3 · Multiply 60 by pi over 180 to get pi over 3.
2 · Arc length is radius times angle: 8 times 0.25 = 2 m.
pi/4 · 45 times pi over 180 is 45 pi over 180, which simplifies to pi over 4.
2 pi · A full turn cuts an arc of the whole circle, which is 2 pi radii.
False · The short formulas only work in radians, so convert first.
6 pi square cm · Half of 36 is 18, and 18 times pi over 3 is 6 pi.
36 · Sector area is half r squared theta: half of 36 times 2 = 36 square metres.
8 · Arc length is r theta, so 4 times 2 is 8.
It must be wrong, since a slice cannot beat the circle · No slice beats its own circle, so check the working for a slip.
pi over 6 · Cosine of pi over 3 is one half, which is sine of pi over 6.