James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A24
appendix D Trigonometry
Angles
Angles can be measured in degrees or in radians (abbreviated as rad). The angle given by
a complete revolution contains 3608, which is the same as 2 rad. Therefore
and
1 rad − 1808
2 1 rad −S D 180 8 < 57.38 18 − rad < 0.017 rad
180
EXAMPLE 1
(a) Find the radian measure of 608.
(b) Express 5y4 rad in degrees.
SOLUTION
(a) From Equation 1 or 2 we see that to convert from degrees to radians we multiply
by y180. Therefore
608 − 60S
180D − 3 rad
(b) To convert from radians to degrees we multiply by 180y. Thus
5
4 rad − 5 4
S 180
D − 2258
■
In calculus we use radians to measure angles except when otherwise indicated. The
fol lowing table gives the correspondence between degree and radian measures of some
common angles.
Degrees 0° 30° 45° 60° 90° 120° 135° 150° 180° 270° 360°
Radians 0
6
4
3
2
2
3
3
4
5
6
3
2
2
r
¨
r
a
Figure 1 shows a sector of a circle with central angle and radius r subtending an arc
with length a. Since the length of the arc is proportional to the size of the angle, and since
the entire circle has circumference 2r and central angle 2, we have
2 −
a
2r
Solving this equation for and for a, we obtain
FIGURE 1
3 − a r
a − r
Remember that Equations 3 are valid only when is measured in radians.
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