Radian and Degree Measure Lesson 1.1 r s = r r If Arc length - - PowerPoint PPT Presentation

Radian and Degree Measure Lesson 1.1

s = r r r

If Arc length (s) = radius, then  = 1 radian.



For one complete revolution,  = 2



0, 2  6.35 rad /2 1.57 rad   3.14 rad 3/2  4.72 rad 1 2 3 4 5 6 Quadrant I Quadrant II Quadrant III Quadrant IV For positive angles

0, - 2  -6.35 rad

• /2  - 1.57 rad
• 
•  - 3.14 rad
• 3/2  - 4.72 rad
• 5
• 4
• 3
• 2
• 1
• 6

Quadrant I Quadrant II Quadrant III Quadrant IV For negative angles

Ex 1: Estimate the angle to the nearest 1/2 radian. A. B. C. 2.5 rad 3.5 rad

• 1 rad

Ex 2: Determine the quadrant in which each angle lies.

• A. /5
• B. 7/5
• C. - /12
• D. - 3.5

Quad I  Quad III Quad IV Quad II

Acute Angles - angles that have a measure 0 <  < /2 radians Obtuse Angles - angles that have a measure /2 <  <  radians

Ex 3: Sketch each angle in standard position.

• A. 2/3
• B. 5/4
• C. - 7/4
• D. 3

Coterminal - two angles that share the same terminal side.    

One positive angle + One negative angle Two positive angles

Ex 4: Determine two co-terminal angles (one positive and one negative) for each angle. A.

/6

+ 2

  6 2      6 12 6  13 6    6 2      6 12 6  11 6 

Ex 4 (cont’d): Determine two co-terminal angles (one positive and one negative) for each angle.

• B. 5/6

5 6 2   

Positive:

  5 6 12 6    17 6 

Negative:

5 6 2      5 6 12 6     7 6 

• C. - 2/3
• D. /12

  2 3 2      2 3 6 3    4 3 

Positive: Negative: 

 2 3 2      2 3 6 3     8 3    12 2      12 24 12  25 12 

Positive: Negative:

  12 2      12 24 12   23 12 

Complementary angles - two angles whose sum is /2 radians Supplementary angles - two angles whose sum is  radians Ex 5: Find, if possible, the complement and supplement

• f each angle
• A. /3

  3 2   x

Compl.:

x     2 3   3 6 2 6     6

Suppl.: 

 3   x x     3   3 3 3    2 3 

Ex 5 (cont’d): Find, if possible, the complement and supplement of each angle

• B. 3/4

3 4 2   

Compl.: Suppl.: 3

4     x x     3 4   4 4 3 4     4

Complementary angle does not exist.

Homework: p.138 #2-24 even

• C. 1
• D. 2

Ex 5 (cont’d): Find, if possible, the complement and supplement of each angle

Compl.:

1 2   x  x    2 1

Suppl.: 1

 x 

x    1

Compl.:

2 2   Does not exist.

Suppl.: 2 

 x 

x    2