Page 32 - Calculus Demystified

Basics
CHAPTER 1

Fig. 1.24 19
1.7 Trigonometry

Here we give a whirlwind review of basic ideas of trigonometry. The reader who
needs a more extensive review should consult [SCH1].
When we first learn trigonometry, we do so by studying right triangles and
measuringanglesindegrees.LookatFig.1.25.Incalculus,however,itisconvenient
to study trigonometry in a more general setting, and to measure angles in radians.

measured in degrees
Fig. 1.25

Angles will be measured by rotation along the unit circle in the plane, beginning
at the positive x-axis. See Fig. 1.26. Counterclockwise rotation corresponds to
positive angles, and clockwise rotation corresponds to negative angles. Refer to
Fig. 1.27. The radian measure of an angle is defined to be the length of the arc
of the unit circle that the angle subtends with the positive x-axis (together with an
appropriate + or − sign).