Radian — Algebra II, what it means and where it is taught
The angle whose arc length equals the radius. A full turn is 2π radians.
Taught in Algebra II.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Radius — Centre to edge. Half the diameter.
- Arc — Part of the edge; a "pizza slice" bounded by two radii.
- π — The circumference of any circle divided by its diameter — about 3.14159.
Practise this idea
8 questions in the course bank use Radian, in Radians & the Unit Circle.
Problem 1
Convert 180° to radians. Give the coefficient of π.
Worked answer
1
180° = π radians
Problem 2
Convert 90° to radians. Give your answer in the form a/b times pi, as the fraction only.
Worked answer
1/2
A
q
u
a
r
t
e
r
t
u
r
n
i
s
h
a
l
f
o
f
\
p
i
.
Problem 3
Convert π4 radians to degrees.
Worked answer
45
1804=45
Problem 4
Convert 2π3 radians to degrees.
Worked answer
120
2 × 1803=120
Problem 5
How many radians are there in a full turn? Give the coefficient of π.
Worked answer
2
2π
Problem 6
Convert 270° to radians. Give the answer as the fraction multiplying π.
Worked answer
3/2
T
h
r
e
e
q
u
a
r
t
e
r
s
o
f
a
t
u
r
n
.
Problem 7
A circle of radius 6 has a central angle of π3. Find the arc length. Give the coefficient of π.
Worked answer
2
6 · π3=2π
Problem 8
A circle of radius 10 has a central angle of 1.5 radians. Find the arc length.
Worked answer
15
10 × 1.5 = 15