Angle Measure Worksheet With Answers - Section 6.1 Page 5
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10EXAMPLE:
(a) Find an angle between 0 and 2π that is coterminal with 100.
◦
◦
◦
(b) Find an angle between 0
and 360
that is coterminal with
3624
.
Solution:
(a) We have
30π ≈ 5.7522
100
(b) We have
◦
◦
◦
◦
◦
+ 11 · 360
3624
=
3624
+ 3960
= 336
88π
EXAMPLE: Find an angle between 0 and 2π that is coterminal with
.
3
Solution: We have
88π
4π
28π =
3
3
◦
◦
EXAMPLE: Find an angle with measure between 0
and 360
that is coterminal with the angle
◦
of measure 1635
in standard position.
Solution: We have
◦
◦
◦
◦
◦
4 · 360
1635
= 1635
+ 1440
= 195
Length of a Circular Arc
An angle whose radian measure is θ is subtended by an arc that is the
fraction θ/(2π) of the circumference of a circle. Thus, in a circle of radius
r, the length s of an arc that subtends the angle θ (see the Figure on the
right) is
θ
θ
× circumference of circle =
s =
(2πr) = θr
2π
2π
Solving for θ, we get the important formula
s
θ =
r
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