Page 34 - Calculus Demystified

Basics
CHAPTER 1
EXAMPLE 1.16 21
Sketch the angle with radian measure π/6. Give itsequivalent degree
measure.
SOLUTION
Since
π/6 1
= ,
2π 12
the angle subtends an arc of the unit circle corresponding to 1/12 of the full cir-
cumference. Since π/6 > 0, the angle represents a counterclockwise rotation.
It is illustrated in Fig. 1.28.

y

p/6
x

Fig. 1.28

The degree measure of this angle is

180 π ◦
· = 30 .
π 6
Math Note: In this book we always use radian measure for angles. (The reason
is that it makes the formulas of calculus turn out to be simpler.) Thus, for example,
if we refer to “the angle 2π/3” then it should be understood that this is an angle in
radian measure. See Fig. 1.29.
Likewise, if we refer to the angle 3 it is also understood to be radian measure.
We sketch this last angle by noting that 3 is approximately 0.477 of a full rotation
2π—refer to Fig. 1.30.

You Try It: Sketch the angles −2, 1, π,3π/2, 10—all on the same coordinate
figure. Of course use radian measure.