Section 2.1 Notes.notebook
1
April 01, 2015
Chapter 2: Trigonometry2.1 Angles in Standard Position
1) Sketch an angle from 0° to 360° in standard position and determine its reference angle.
2) Determine the quadrant in which an angle in standard position terminates.
3) Determine the exact values of the sine, cosine, and tangent ratios for 304560
4) Solve problems involving trig ratios.
Section 2.1 Notes.notebook
2
April 01, 2015
Work with a partner and answer questions 15 on page 75
Section 2.1 Notes.notebook
3
April 01, 2015
Section 2.1 Notes.notebook
4
April 01, 2015
Section 2.1 Notes.notebook
5
April 01, 2015
0180
10170
20160
30
15040
140 50
13060
120
70
110
80
100
90
90
180°
100
80
110
70
120
60
130
50
140
40
150
30
16020
170 10
180 0
Section 2.1 Notes.notebook
6
April 01, 2015
initial arm (ray)
terminal arm (ray)
angle in standard position
the arm of an angle in standard position that lies on the positive xaxis
the arm of an angle in standard position that meets the initial arm at the origin to form an angle.
the position of an angle when its initial arm is on the positive xaxis and its vertex is at the origin
Section 2.1 Notes.notebook
7
April 01, 2015
reference angle
Note:The trigonometric ratios of an angle in standard position are the same as the trigonometric ratios of its reference angle except that they may differ in sign.
the positive acute angle whose vertex is the origin and whose arms are the terminal arm of the angle and the xaxis.
Section 2.1 Notes.notebook
8
April 01, 2015
Section 2.1 Notes.notebook
9
April 01, 2015
Lesson Focus: Angle in Standard Position
2.1 Angles in Standard Position
2.1 Angles in Standard Position
Example 1 Page 79Sketch an Angle in Standard Position
Sketch each angle in standard position. State the quadrant inwhich the terminal arm lies. a﴿ 36° b﴿ 210° c﴿ 315°
Section 2.1 Notes.notebook
10
April 01, 2015
Lesson Focus: Labels
2.1 Angles in Standard Position
2.1 Angles in Standard Position
RInitial Arm
Terminal Arm
Reference AngleAngle in Standard Position
Quadrants
I
II
III IV
Drag to label the parts of the diagram.
Section 2.1 Notes.notebook
11
April 01, 2015
Lesson Focus: Reference Angle
2.1 Angles in Standard Position
2.1 Angles in Standard Position
Example 2 Page 80Determine a Reference AngleDetermine the reference angle θR for each angle θ. Sketch θ in standard position and label the reference angle θR.a﴿ θ = 130° b﴿ θ = 300°
Section 2.1 Notes.notebook
12
April 01, 2015
θR= 180o - θ θR= θ
θR= θ - 180oθR= 360o - θ
exact values answers that involve terminating decimals, fractions or radicals. answers that are rounded are approximations and are NOT exact.
Section 2.1 Notes.notebook
13
April 01, 2015
Determine the angle in standard position when an angle of 40° is reflectedb﴿ in the xaxis
Determine the angle in standard position when an angle of 40° is reflecteda﴿ in the yaxis
Determine the angle in standard position when an angle of 40° is reflectedc﴿ in the yaxis and then in the xaxis
Section 2.1 Notes.notebook
14
April 01, 2015
Special Triangles
45o 45o 90o Triangle
45o
45o
1
Calculate the exact value of c
c
1
Section 2.1 Notes.notebook
15
April 01, 2015
Equilateral triangle:
60o 60o
60o
2
22
a
Calculate the altitude of the equilateral triangle
Section 2.1 Notes.notebook
16
April 01, 2015
Lesson Focus: Special Triangles and Exact Values
2.1 Angles in Standard Position
2.1 Angles in Standard Position
30o
60o
2
1
45o
45o
1
1
30o 45o 60o
Section 2.1 Notes.notebook
17
April 01, 2015
Find an Exact DistanceAllie is learning to play the piano. Her teacher uses a metronome to help her keep time. The pendulum arm of the metronome is 10 cm long. For one particular tempo, the setting results in the arm moving back and forth from a start position of 60° to 120°. What horizontal distance does the tip of the arm move in one beat? Give an exact answer.
Section 2.1 Notes.notebook
18
April 01, 2015
Pgs: 8385: #’s 19, 11, 13, 14, 17