1. 13.2 - Define General Angles and Radian Measure
Page 856 3) 5) 7) 9)
11)
13)
15) C
17)
x = 8√3, y = 16
19)
x = 4√3, y = 8√3
21)
B = 55°, a ≈ 9.177, b ≈
23)
A = 72°, a ≈ , b ≈ 7.416
25)
A = 15°, b ≈ , c ≈
27)
B = 26°, a ≈ , c ≈
32)
Height: ft, Length: ft
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Define General Angles and Radian Measure

2. 13.2 - Define General Angles and Radian Measure
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Define General Angles and Radian Measure

3. Define General Angles and Radian Measure
Section 13.2
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Define General Angles and Radian Measure

4. 13.2 - Define General Angles and Radian Measure
Definitions
Angle of Rotation is formed by two rays with a common endpoint, also called the vertex.
One ray is called the initial side.
The other ray is called the terminal side.
The measure of the angle is determined by the amount and direction of rotation from the initial side to the terminal side.
Coterminal angles are angles in standard position with the same terminal side
To determine the coterminal angles, add and/or subtract 360° (Magic Number is 360°)
Coterminal angles can be negative
There are an infinite amount of coterminal angles
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Define General Angles and Radian Measure

5. 13.2 - Define General Angles and Radian Measure
Example 1
Draw 210° with the given measure in standard position. Then, determine which quadrant the terminal side lies.
Label the axis when drawing angles
Must draw the angle and its arrow (to indicate both the direction) receive full credit
210°
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Define General Angles and Radian Measure

6. 13.2 - Define General Angles and Radian Measure
Example 2
Draw –45° with the given measure in standard position. Then, determine in which quadrant the terminal side lies.
–45°
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Define General Angles and Radian Measure

7. 13.2 - Define General Angles and Radian Measure
Example 3
Draw 510° with the given measure in standard position. Then, determine in which quadrant the terminal side lies.
Get the actual angle 510° - 360° = 150°
So the terminal side makes 1 complete revolution and continues another 150°.
150°
510°
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Define General Angles and Radian Measure

8. 13.2 - Define General Angles and Radian Measure
Your Turn
Draw 400° with the given measure in standard position. Then, determine in which quadrant the terminal side lies.
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Define General Angles and Radian Measure

9. 13.2 - Define General Angles and Radian Measure
Example 4
Find the measures of a positive and negative angles that are coterminal with ө = 40°.
Magic Number:
360°
40°
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Define General Angles and Radian Measure

10. 13.2 - Define General Angles and Radian Measure
Example 5
Find the measures of a positive and negative angles that are coterminal with ө = 65°
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Define General Angles and Radian Measure

11. 13.2 - Define General Angles and Radian Measure
Your Turn
Find the measures of a positive and negative angles that are coterminal with ө = 740°
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Define General Angles and Radian Measure

12. 13.2 - Define General Angles and Radian Measure
Degree measure is a unit of application such as surveying and navigation
Radian measure is a unit of measure for theoretical work in mathematics. Before angles, they measured in Radian Measure
One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length, r. r r
one radian
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Define General Angles and Radian Measure

13. 13.2 - Define General Angles and Radian Measure
Conversions
To convert degrees to radians, multiply π/180°
To convert radians to degrees, multiply 180°/π
180° = π Radian
1° = π/180 Radian
180°/π = 1 Radian
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Define General Angles and Radian Measure

14. 13.2 - Define General Angles and Radian Measure
Example 6
Convert 240° into radian measure
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Define General Angles and Radian Measure

15. 13.2 - Define General Angles and Radian Measure
Example 7
Convert –90° into radian measure
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Define General Angles and Radian Measure

16. 13.2 - Define General Angles and Radian Measure
Your Turn
Convert 2° into radian measure
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Define General Angles and Radian Measure

17. 13.2 - Define General Angles and Radian Measure
Example 8
Convert 9π/2 into degree measure
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Define General Angles and Radian Measure

18. 13.2 - Define General Angles and Radian Measure
Example 9
Convert 1 Radian into degree measure
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Define General Angles and Radian Measure

19. Arc Length and Area of Sector
Sector is a region of the circle that bounded by two radii and an arc of a circle
The Central Angle of a sector is the angle formed by the two radii
Arc Length equation: s = r ө
Area of a Sector: A = (r2ө)/2
Degrees must be converted to Radians
Arc Length, s
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Define General Angles and Radian Measure

20. 13.2 - Define General Angles and Radian Measure
Example 10
Determine the Arc Length and Area of Sector with the given radius of r = 4 inches and ө = π/6.
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Define General Angles and Radian Measure

21. 13.2 - Define General Angles and Radian Measure
Example 11
Determine the Arc Length and Area of Sector with the given radius of r = 15 inches and ө = 45°.
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Define General Angles and Radian Measure

22. 13.2 - Define General Angles and Radian Measure
Example 12
Determine the Arc Length and Area of Sector with the given radius of r = 180 feet and ө = 90°.
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Define General Angles and Radian Measure

23. 13.2 - Define General Angles and Radian Measure
Your Turn
Determine the Arc Length and Area of Sector with the given radius of r = 8 inches and ө = 115°.
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Define General Angles and Radian Measure

24. 13.2 - Define General Angles and Radian Measure
Assignment
Page 862
3-37 odd, leave π form
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Define General Angles and Radian Measure