Transcript Holt McDougal Algebra 2

Angles
AnglesofofRotation
Rotation
• How do we draw angles in standard
position?
• How do we determine the values of the
trigonometric functions for an angle in
standard position?
HoltMcDougal
Algebra 2Algebra 2
Holt
Angles of Rotation
For an angle θ in standard position,
the reference angle is the positive
acute angle formed by the terminal
side of θ and the x-axis. Later, you
will learn how to use reference angles
to find trigonometric values of angles
measuring greater than 90° or less
than 0°.
Holt McDougal Algebra 2
Angles of Rotation
Finding Reference Angles
Find the measure of the reference angle for each given angle.
1.  = 135°
180 135
o
45
The measure of the
reference angle is 45°.
Holt McDougal Algebra 2
2.  = –105°
180 105
75o
–105°
The measure of the
reference angle is 75°.
Angles of Rotation
Finding Reference Angles
Find the measure of the reference angle for each given angle.
3.  = 325°
360  325
o
35
The measure of the
reference angle is 35°.
Holt McDougal Algebra 2
4.  = –115°
180 115
65o
–115°
The measure of the
reference angle is 65°.
Angles of Rotation
Finding Reference Angles
Find the measure of the reference angle for each given angle.
5.  = 310°
310°
360  310
o
50
The measure of the
reference angle is 50°.
Holt McDougal Algebra 2
6.  = 105°
180 105
75o
105°
The measure of the
reference angle is 75°.
Angles of Rotation
To determine the value of
the trigonometric functions
for an angle θ in standard
position, begin by selecting
a point P with coordinates
(x, y) on the terminal side
of the angle. The distance r
from point P to the origin is
given by
.
Holt McDougal Algebra 2
Angles of Rotation
Finding Values of Trigonometric Functions
Using a point on the terminal side of  in standard position, find
the exact value of the six trigonometric functions for θ.
7. P (–6, 9)
 6, 9
sin 
cos 
tan 
9
3


3 13 13
6 2


3 13 13
9
3


6
2
Holt McDougal Algebra 2
13
csc  
3
13
sec  
2
cot 
2

3
3 13
9
6
 6   9 
36  81
117  3 13
2
2
Angles of Rotation
Finding Values of Trigonometric Functions
Using a point on the terminal side of  in standard position, find
the exact value of the six trigonometric functions for θ.
8. P (–3, 6)
 3, 6
sin 
cos 
tan 
6
2


5
3 5
3
1


5
3 5
6

 2
3
Holt McDougal Algebra 2
csc 
5

2
3 5
6
sec    5
3
 3  6
9  36
45  3 5
2
cot 
1

2
2
Angles of Rotation
Finding Values of Trigonometric Functions
Using a point on the terminal side of  in standard position, find
the exact value of the six trigonometric functions for θ.
9. P (–15, –8)
sin  
8
cos 
17
 15

17
tan 
8

 15
 15
17  8
csc   
17
8
15,  8
17
sec   
15
2
2




8
 15
8
225  64
8

cot  
 17
289
15
15
Holt McDougal Algebra 2
Angles of Rotation
Lesson 10.2 Practice B
Holt McDougal Algebra 2