The Trigonometric Functions

1
Chapter 5

• The Trigonometric Functions

2
5-1 Angles and Degree Measure
Terminal Side
?
Initial Side
3
standard position
120
4
counterclockwise
clockwise
330
-225
positive angle
negative angle
5
90
Quadrant I
Quadrant II
180
0
360
Quadrant III
Quadrant IV
270
6
Quadrant I
Quadrant II
90
135
60
180
0
360
-135
270
Quadrant III
7
90
180
0
360
300
Quadrant IV
270
8
Coterminal Angles

• Two angles in standard position are called
  coterminal angles if they have the same terminal
  side.
• Any angle has an infinite number of coterminal
  angles.

9
Coterminal Angles
70
430
70 360 430
10
70 2(360) 70 720 790
70
790
11
70 - 360 -290
70
-290
12
Cotermial Angles

• Sketch each angle in standard position and find
  one positive and negative coterminal angle.

y

• Example
• -100
• -100 360 260
• -100 - 360 -460

x
13

• Sketch each angle in standard position and find
  one positive and one negative coterminal angle.

1) 180 2) -502 3) 1305
14
Reference Angle

• The acute angle formed by the terminal side of
  the given angle ? and the x-axis.

?
?
?
?
15

• For an angle ?, 0 lt ? lt 360 it reference angle
  is defined by

a. ?, when the terminal side lies in quadrant I.
I
80
16

• b. 180 - ?, when the terminal side lies in
  quadrant II.

II
145
35
180 - 145 35
17

• ? - 180, when the terminal side
• lies in quadrant III

260
80
260 - 180 80
III
18

• d. 360 - ?, when the terminal side lies in
  quadrant IV

360 - 315 45
45
315
IV