1. 1.1
Angles
Basic Terminology ▪ Degree Measure ▪ Standard Position ▪ Coterminal Angles
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2. 1.1 Example 1 Finding the Complement and the Supplement of an Angle (page 3)
For an angle measuring 55°, find the measure of its complement and its supplement.
Complement: 90° − 55° = 35°
Supplement: 180° − 55° = 125°
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3. Find the measure of each angle.
1.1 Example 2(a) Finding Measures of Complementary and Supplementary Angles (page 3)
Find the measure of each angle.
The two angles form a right angle, so they are complements.
The measures of the two angles are
and
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4. Find the measure of each angle.
1.1 Example 2(b) Finding Measures of Complementary and Supplementary Angles (page 3)
Find the measure of each angle.
The two angles form a straight angle, so they are supplements.
The measures of the two angles are
and
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5. 1.1 Example 3 Calculating with Degrees, Minutes, and Seconds (page 4)
Perform each calculation.
(a)
(b)
180˚ 0′
–117˚29′
179˚60′
–117˚29′
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6. (a) Convert 105°20′32″ to decimal degrees.
1.1 Example 4 Converting Between Decimal Degrees and Degrees, Minutes, and Seconds (page 5)
(a) Convert 105°20′32″ to decimal degrees.
(b) Convert ° to degrees, minutes, and seconds.
Show them how to use the M+ and Mc on basic
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7. 1.1 Example 5 Finding Measures of Coterminal Angles (page 6)
Find the angles of least possible positive measure coterminal with each angle.
Add or subtract 360° as many times as needed to obtain an angle with measure greater than 0° but less than 360°.
(a) 1106°
An angle of 1106° is coterminal with an angle of 26°.
(b) –150°
An angle of –150° is coterminal with an angle of 210°.
(c) –603°
An angle of –603° is coterminal with an angle of 117°.

8. 1.1 Example 6 Analyzing the Revolutions of a CD Player (page 7)
A wheel makes 270 revolutions per minute. Through how many degrees will a point on the edge of the wheel move in 5 sec?
The wheel makes 270 revolutions in one minute or revolutions per second.
In five seconds, the wheel makes revolutions.
Each revolution is 360°, so a point on the edge of the wheel will move
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9. 1.1 Summary
Supplementary: two angles with a sum of 180˚ Complementary: two 2 angles with a sum of 90˚ Convert from decimal degrees to degrees, minutes, & seconds Convert from degrees, minutes, & seconds to decimal degrees Coterminal angles ± 360˚
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10. 1.2 Angles Geometric Properties ▪ Triangles
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11. 1.2 Example 1 Finding Angle Measures (page 12)
Find the measures of angles 1, 2, 3, and 4 in the figure, given that lines m and n are parallel.
Angles 2 and 3 are same side interior, so they are supplements.

12. 1.2 Example 5 Finding the Height of a Tree (page 15)
Samir wants to know the height of a tree in a park near his home. The tree casts a 38-ft shadow at the same time as Samir, who is 63 in. tall, casts a 42-in. shadow. Find the height of the tree.
Let x = the height of the tree
The tree is 57 feet tall.
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13. 1.2 summary Geometric properties and Similar Triangles
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14. Trigonometric Functions
1.3
Trigonometric Functions
Trigonometric Functions ▪ Quadrantal Angles
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15. Trigonometry Rules Need to memorize: Soh Cah Toa Sin θ = y/r r Cos θ =
x/r y θ
Tan θ =
y/x x
Csc θ =
r/y
Sec θ =
r/x
Cot θ =
x/y
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16. 1.3 Example 1 Finding Function Values of an Angle (page 23)
The terminal side of an angle θ in standard position passes through the point (12, 5). Find the values of the six trigonometric functions of angle θ.
x = 12 and y = 5. 13
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17. 1.3 Example 2 Finding Function Values of an Angle (page 23)
The terminal side of an angle θ in standard position passes through the point (8, –6). Find the values of the six trigonometric functions of angle θ.
x = 8 and y = –6. 10
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18. 1.3 Example 3 Finding Function Values of an Angle (page 25)
Find the values of the six trigonometric functions of angle θ in standard position, if the terminal side of θ is defined by 3x – 2y = 0, x ≤ 0.
Since x ≤ 0, the graph of the line 3x – 2y = 0 is shown to the left of the y-axis.
Find a point on the line: Let x = –2. Then
A point on the line is (–2, –3).
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19. 1.3 Example 3 Finding Function Values of an Angle (cont.)
Point (-2,-3) -2 -3
√13
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20. Find the values of the six trigonometric functions of a 360° angle.
1.3 Example 4(a) Finding Function Values of Quadrantal Angles (page 26)
Find the values of the six trigonometric functions of a 360° angle.
The terminal side passes through (2, 0). So x = 2 and y = 0 and r = 2.
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21. 1.3 Example 4(b) Finding Function Values of Quadrantal Angles (page 26)
Find the values of the six trigonometric functions of an angle θ in standard position with terminal side through (0, –5).
x = 0 and y = –5 and r = 5.
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22. 1.3 Summary Trigonometry Rules
Need to memorize: Soh Cah Toa
Sin θ =
y/r r
Cos θ =
x/r y θ
Tan θ =
y/x x
Csc θ =
r/y
Sec θ =
r/x
Cot θ =
x/y
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23. Using the Definitions of the Trigonometric Functions
1.4
Using the Definitions of the Trigonometric Functions
Reciprocal Identities ▪ Signs and Ranges of Function Values ▪ Pythagorean Identities ▪ Quotient Identities
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24. 1.4 Example 1 Using the Reciprocal Identities (page 31)
Find each function value.
(a) tan θ, given that cot θ = 4.
tan θ is the reciprocal of cot θ.
(b) sec θ, given that
sec θ is the reciprocal of cos θ.
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25. All Students Take Calculus
Need to memorize:
Students
+ sin
- cos & tan
All
+ sin, cos, & tan
+ csc
- sec & cot
Take
+ tan
- cos & sin
Calculus
+ cos
- sin & tan
+ cot
- sec & csc
+ sec
- csc & cot
Which others are also positive and negative? (the reciprocals)
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26. 1.4 Example 2 Finding Function Values of an Angle (page 32)
Determine the signs of the trigonometric functions of an angle in standard position with the given measure.
(a) 54° (b) 260° (c) –60°
Students
Students
All
+ sin, cos, & tan
+ csc, sec, cot
All
Students
All
Take
Calculus
Take
+ tan, cot
- sin, cos, sec, csc
Calculus
Take
Calculus
+ cos, sec
- sin, tan, csc, cot
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27. 1.4 Example 3 Identifying the Quadrant of an Angle (page 33)
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions.
(a) tan θ > 0, csc θ < 0
Where is the tan positive and csc negative
Where is the tan positive and sin negative
Answer: Quadrant III II I
Students
All
Take
Calculus
(b) sin θ > 0, csc θ > 0
III IV
Where is the sin positive and csc positive
Where is the sin positive and sin positive
Answer: Quadrant I & II
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28. Need to Memorize
Tan and Cot range = (-∞,∞) Sin and Cos range = [-1,1] Csc and Sec range = (-∞,-1] [1,∞) ∩
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29. Decide whether each statement is possible or impossible.
1.4 Example 4 Deciding Whether a Value is in the Range of a Trigonometric Function (page 33)
Use the picture to show why
Decide whether each statement is possible or impossible.
(a) cot θ = – (b) cos θ = –1.7 (c) csc θ = 0
(a) cot θ = –.999 is possible because the range of cot θ is
cot θ = tan θ = -1/ θ = tan-1 (-1/.999)
(b) cos θ = –1.7 is impossible because the range of cos θ is [–1, 1].
cos θ = θ = cos-1 (-1.7) = error
(c) csc θ = 0 is impossible because the range of csc θ is
csc θ = 0 sin θ = 1/0 1/0 undefined

30. 1.4 Example 5 Finding All Function Values Given One Value and the Quadrant (page 33)
Angle θ lies in quadrant III, and Find the values of the other five trigonometric functions.
Since θ lies in quadrant III, then x is negative and y is negative
x=-5 θ
y=-8 r=
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31. Find cos θ and tan θ given that sin θ and cos θ > 0.
1.4 Example 6 Finding Other Function Values Given One Value and the Quadrant (page 35)
Find cos θ and tan θ given that sin θ and cos θ > 0.
Find which quadrant first? Where is the sin negative and cos positive? x= θ y=
r=3
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32. Find cot θ and csc θ given that cos θ and θ is in quadrant II.
1.4 Example 7 Finding Other Function Values Given One Value and the Quadrant (page 36)
Find cot θ and csc θ given that cos θ and θ is in quadrant II.
Since θ is in quadrant II, x is negative and y is positive
r=25
y=24 θ
x=-7
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33. Additional Example
Given csc θ = and θ is in quadrant II, find cot θ
Since csc θ = , then sin θ = 1/ r=
x = -√( – 12) =
y=1 θ x=
Need to find the cot θ which is x/y
cot θ =
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34. 1.4 Summary Trigonometry Rules
Need to memorize: Soh Cah Toa
Students
All
Sin θ =
y/r r
Cos θ =
x/r y θ
Tan θ =
y/x x
Csc θ =
r/y
Take
Calculus
Sec θ =
r/x
Cot θ =
x/y
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.