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Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.

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Presentation on theme: "Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures."— Presentation transcript:

1 Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures

2 Copyright © 2011 Pearson, Inc. Slide 4.1 - 2 Why 360º ? θ is a central angle intercepting a circular arc of length a. The measure can be in degrees (a circle measures 360º once around) or in radians, which measures the length of arc a.

3 Copyright © 2011 Pearson, Inc. Slide 4.1 - 3 Radian A central angle of a circle has measure 1 radian if it intercepts an arc with the same length as the radius.

4 Copyright © 2011 Pearson, Inc. Slide 4.1 - 4 Degree-Radian Conversion

5 Copyright © 2011 Pearson, Inc. Slide 4.1 - 5 Example Working with Degree and Radian Measure a. How many radians are in 135º? b. How many degrees are in radians? c. Find the length of an arc intercepted by a central angle of 1/4 radian in a circle of radius 3 in.

6 Copyright © 2011 Pearson, Inc. Slide 4.1 - 6 Example Working with Degree and Radian Measure a. How many radians are in 135º?

7 Copyright © 2011 Pearson, Inc. Slide 4.1 - 7 Example Working with Degree and Radian Measure b. How many degrees are in radians?

8 Copyright © 2011 Pearson, Inc. Slide 4.1 - 8 Example Working with Degree and Radian Measure A central angle of 1 radian intercepts an arc length of 1 radius, which is 3 in. So a central angle of 1/4 radian intercepts an arc of length 1/4 radius, which is 3/4 in. c. Find the length of an arc intercepted by a central angle of 1/4 radian in a circle of radius 3 in.

9 Copyright © 2011 Pearson, Inc. Slide 4.1 - 9 Arc Length Formula (Radian Measure)

10 Copyright © 2011 Pearson, Inc. Slide 4.1 - 10 Arc Length Formula (Degree Measure)

11 Copyright © 2011 Pearson, Inc. Degrees, Minutes, and Seconds Converting to DMS from decimal form. Take the decimal form from the origional equation and multiply by 60’. Take the decimal form from step one and multiply by 60”. Slide 4.1 - 11

12 Copyright © 2011 Pearson, Inc. Degrees, Minutes, and Seconds Converting from DMS to decimal form. Take the decimal form from the origional equation and divide by 60’. Take the decimal form from step one and divide by 60”. Slide 4.1 - 12

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