Chapter 1 | Functions and Graphs
63
Degrees Radians Degrees Radians
2 π /3
0
0
120
π /6
3 π /4
30
135
π /4
5 π /6
45
150
π /3
π
60
180
π /2
90
Table 1.8 Common Angles Expressed in Degrees and Radians
Example 1.22 Converting between Radians and Degrees a. Express 225° using radians. b. Express 5 π /3 rad using degrees.
Solution Use the fact that 180° is equivalent to π radians as a conversion factor: 1= π rad 180° =
180° π rad
.
a. 225° = 225° · π
5 π 4
rad
180° =
b. 5 π 3
rad = 5 π
180°
π =300°
3 ·
Express 210° using radians. Express 11 π /6 rad using degrees.
1.17
The Six Basic Trigonometric Functions Trigonometric functions allow us to use angle measures, in radians or degrees, to find the coordinates of a point on any circle—not only on a unit circle—or to find an angle given a point on a circle. They also define the relationship among the sides and angles of a triangle. To define the trigonometric functions, first consider the unit circle centered at the origin and a point P = ( x , y ) on the unit circle. Let θ be an angle with an initial side that lies along the positive x -axis and with a terminal side that is the line segment OP . An angle in this position is said to be in standard position ( Figure 1.31 ). We can then define the values of the six trigonometric functions for θ in terms of the coordinates x and y .
Made with FlippingBook - professional solution for displaying marketing and sales documents online