Download chapter 1 power points

Chapter 1
Trigonometric Functions
Copyright © 2005 Pearson Education, Inc.
Section1.1- Angles
Objective: SWBAT learn the basic terminology of
angles and their degree measures. In addition students
will be able to determine an angle in standard position
with coterminal angles.
Copyright © 2005 Pearson Education, Inc.
Basic Terms
Two distinct points determine a line called
line AB.
A
B
Line segment AB—a portion of the line between
A and B, including points A and B.
A
B
Ray AB—portion of line AB that starts at A and
continues through B, and on past B.
A
Copyright © 2005 Pearson Education, Inc.
B
Slide 1-3
Basic Terms continued…

Angle-formed by rotating
a ray around its endpoint.

The ray in its initial
position is called the
initial side of the angle.

The ray in its location
after the rotation is the
terminal side of the
angle.

Vertex-the endpoint of
the ray
Copyright © 2005 Pearson Education, Inc.
Slide 1-4
Basic Terms continued…

Positive angle: The
rotation of the terminal
side of an angle
counterclockwise.
Copyright © 2005 Pearson Education, Inc.

Negative angle: The
rotation of the terminal
side is clockwise.
Slide 1-5
Naming an Angle
An angle can be named using its vertex.
Ex: angle C
C
.
.
A
B
.
An angle also can be named using 3 letters with
the vertex in the middle.
Ex: angle ACB or angle BCA
Copyright © 2005 Pearson Education, Inc.
Slide 1-6
Types of Angles

The most common unit for measuring angles is
the degree. 360° for a complete rotation of a
ray. 1 ° = 1/360 of a rotation. θ is used to name
an angle.
Copyright © 2005 Pearson Education, Inc.
Slide 1-7
Complementary &
Supplementary Angles
Two positive angles whose sum is 90° are called
complementary angles.
Two positive angles whose sum is 180°
are called supplementary angles.
Copyright © 2005 Pearson Education, Inc.
Slide 1-8
Complementary Angles


Find the measure of each angle.
Since the two angles form a right
angle, they are complementary
angles. Thus,
k  20  k  16  90
2k  4  90
2k  86
k  43
Copyright © 2005 Pearson Education, Inc.
k +20
k  16
The two angles have measures of
43 + 20 = 63 and 43  16 = 27
Slide 1-9
Supplementary Angles


Find the measure of each angle.
Since the two angles form a straight
angle, they are supplementary
angles. Thus,
6 x  7  3 x  2  180
9 x  9  180
9 x  171
x  19
Copyright © 2005 Pearson Education, Inc.
6x + 7
3x + 2
These angle measures are
6(19) + 7 = 121 and 3(19) + 2 = 59
Slide 1-10
Degree, Minutes, Seconds
Portions of a degree are measured in minutes and
seconds.

One minute is 1/60 of a degree.
1
1' 
60

60'  1
or
One second is 1/60 of a minute.
1
1
1" 

60 3600
or
60"  1'
12° 42’ 38” represents 12 degrees, 42 minutes, 38 seconds.
Copyright © 2005 Pearson Education, Inc.
Slide 1-11
Calculations

Perform the calculation.
27 34' 26 52'

Perform the calculation.
72  15 18'
27 34'

 26 52'
53 86'

Write 72 as 71 60'
71 60
Since 86 = 60 + 26, the
sum is written
53
15 18'
 1 26'
56 42'
54 26'
Copyright © 2005 Pearson Education, Inc.
Slide 1-12
Conversions
Converting between decimal degrees and degrees, minutes & seconds.

Convert
74 12' 18"
12
18
74 12' 18"  74 

60 3600
 74  .2  .005
 74.205

Convert 36.624
34.624  34  .624
 34  .624(60')
 34  37.44'
 34  37 ' .44'
 34  37 ' .44(60")
 34  37 ' 26.4"
 34 37 ' 26.4"
Copyright © 2005 Pearson Education, Inc.
Slide 1-13
Warm up

Convert 74° 8’ 14” to decimal degrees.

Convert 34.817° to degrees, minutes, and
seconds.
Copyright © 2005 Pearson Education, Inc.
Slide 1-14
Section1.1- Angles
Objective: SWBAT learn the basic terminology of
angles and their degree measures. In addition students
will be able to determine an angle in standard position
with coterminal angles.
Copyright © 2005 Pearson Education, Inc.
Standard Position

An angle is in standard position if its vertex is
at the origin and its initial side is along the
positive x-axis.

Angles in standard position having their terminal
sides along the x-axis or y-axis, such as angles
with measures 90, 180, 270, and so on, are
called quadrantal angles.
Copyright © 2005 Pearson Education, Inc.
Slide 1-16
Coterminal Angles

A complete rotation of a ray results in an angle
measuring 360. By continuing the rotation,
angles of measure larger than 360 can be
produced. Such angles are called coterminal
angles.
Copyright © 2005 Pearson Education, Inc.
Slide 1-17
Coterminal Angles




Find the angles of smallest possible positive
measure coterminal with each angle.
a) 1115
b) 187
Add or subtract 360 as may times as needed to
obtain an angle with measure greater than 0 but
less than 360.
o
o
o
a) 1115  3(360 )  35
b) 187 + 360 = 173
Copyright © 2005 Pearson Education, Inc.
Slide 1-18
Homework

Worksheet left side
Copyright © 2005 Pearson Education, Inc.
Slide 1-19