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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.
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Work with a partner and answer questions 15 on page 75
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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
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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
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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.
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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°
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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.
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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°
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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.
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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
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Special Triangles
45o 45o 90o Triangle
45o
45o
1
Calculate the exact value of c
c
1
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Equilateral triangle:
60o 60o
60o
2
22
a
Calculate the altitude of the equilateral triangle
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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
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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.
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Pgs: 8385: #’s 19, 11, 13, 14, 17
