1. Radian and Degree Measure
Section 4.1
Precalculus PreAP/Dual, Revised ©2017
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§4.1: Radian and Degree Measure

2. What is a Degree and Radian Measure?
𝟏° B. 𝝅 Radian C. 1 Radian
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§4.1: Radian and Degree Measure

3. §4.1: Radian and Degree Measure
What is a Radian?
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§4.1: Radian and Degree Measure

4. §4.1: Radian and Degree Measure
Conversions
180° = 𝝅 Radian
1° = 𝝅 𝟏𝟖𝟎 Radian
𝟏𝟖𝟎 𝝅 = 1 Radian
Conversions between Degrees and Radians:
Rewrite degrees as radians, multiply 𝝅 𝟏𝟖𝟎
Rewrite radians as degrees, multiply 𝟏𝟖𝟎 𝝅
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§4.1: Radian and Degree Measure

5. §4.1: Radian and Degree Measure
Example 1
Convert 240° to radian measure 4 3
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§4.1: Radian and Degree Measure

6. §4.1: Radian and Degree Measure
Example 2
Convert 𝟗𝝅 𝟐 to degree measure 90 1
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§4.1: Radian and Degree Measure

7. §4.1: Radian and Degree Measure
Your Turn
Convert −𝟐° to radian measure
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§4.1: Radian and Degree Measure

8. §4.1: Radian and Degree Measure
Example 3
Convert 1 radian to degree measure
1 radian is not 𝝅 radian
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§4.1: Radian and Degree Measure

9. §4.1: Radian and Degree Measure
Your Turn
Convert 𝟏 𝟒 radian to degree measure
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§4.1: Radian and Degree Measure

10. §4.1: Radian and Degree Measure
Quadrants
For 𝜽 be an angle in standard position with any point 𝒙, 𝒚 :
Quadrant II
−, +
Quadrant I
+, +
Quadrant III
(−, −)
Quadrant IV
+, −
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§4.1: Radian and Degree Measure

11. §4.1: Radian and Degree Measure
Angle of Rotation
Angle of rotation is formed by two rays with a common endpoint (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.
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§4.1: Radian and Degree Measure

12. §4.1: Radian and Degree Measure
Example 4
Draw 𝟐𝟏𝟎° with the given measure in standard position. Then determine in which quadrant the terminal side lies.
𝟐𝟏𝟎°
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§4.1: Radian and Degree Measure

13. §4.1: Radian and Degree Measure
Example 5
Draw 𝟗𝝅 𝟓 with the given measure in standard position. Then determine in which quadrant the terminal side lies.
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§4.1: Radian and Degree Measure

14. §4.1: Radian and Degree Measure
Your Turn
Draw − 𝝅 𝟒 with the given measure in standard position. Then determine in which quadrant the terminal side lies.
−/𝟒
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§4.1: Radian and Degree Measure

15. Complementary and Supplementary
Complementary angles are two angles that add up to 90°
Supplementary angles are two angles that add up to 180°
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§4.1: Radian and Degree Measure

16. §4.1: Radian and Degree Measure
Example 6
Determine the complementary and supplementary angles for 𝝅 𝟏𝟐
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§4.1: Radian and Degree Measure

17. §4.1: Radian and Degree Measure
Example 7
Determine the complementary and supplementary angles for 3 Radians
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§4.1: Radian and Degree Measure

18. §4.1: Radian and Degree Measure
Your Turn
Determine the complementary and supplementary angles for 𝝅 𝟓
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§4.1: Radian and Degree Measure

19. §4.1: Radian and Degree Measure
Coterminal Angles
Coterminal angles are angles in standard position with the same terminal side
To determine the coterminal angles, add and/or subtract 𝟑𝟔𝟎° by rotating counter clockwise for a positive rotation
Coterminal Angles can also be negative
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§4.1: Radian and Degree Measure

20. §4.1: Radian and Degree Measure
Example 8
Find two coterminal rays (1 positive and 1 negative) of 𝟒𝟎°
𝟒𝟎°
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§4.1: Radian and Degree Measure

21. §4.1: Radian and Degree Measure
Example 9
Find one positive and one negative coterminal angle of 𝟕𝝅 𝟑 .
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§4.1: Radian and Degree Measure

22. §4.1: Radian and Degree Measure
Your Turn
Find one positive and one negative coterminal angle of − 𝟕𝝅 𝟗
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§4.1: Radian and Degree Measure

23. §4.1: Radian and Degree Measure
Assignment
Page odd (omit 21, 23)
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§4.1: Radian and Degree Measure