Download presentation

Presentation is loading. Please wait.

Published byOswin Archibald Lambert Modified over 2 years ago

1
Radians Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los Angeles College. All rights reserved. Click one of the buttons below or press the enter key

2
A radian is defined as the length of a circular arc that is equal to the radius of the circle. EXIT BACKNEXT

3
If we choose a circle with a radius of 1, the circle is referred to as a unit circle. If a central angle of the unit circle intercepts an arc with length 1 then the measure of the central angle is 1 radian. So, we can use arc length to measure angles. EXIT BACKNEXT

4
Arc Length on a Unit Circle If you walked along the arc of this circle, one complete revolution, you would have walked a distance of 2 units. EXIT BACKNEXT

5
Why? For any circle of radius r: c = 2 r so in a circle with radius 1 c = 2 (1) = 2 EXIT BACKNEXT

6
How far would one travel if they walked half way around the unit circle? EXIT BACKNEXT

7
How far would one travel if they walked one-quarter the distance around the unit circle? EXIT BACKNEXT

8
What does the distance traveled along the arc of a unit circle have to do with radians? EXIT BACKNEXT

9
The radian system of measurement is based on using arc length: is the distance traveled along the arc of a unit circle. EXIT BACKNEXT

10
This means that if the central angle measures 90 , this angle is equivalent to radians. To illustrate... EXIT BACKNEXT

11
90 radians ¼ revolution ccw EXIT BACKNEXT

12
180 radians ½ revolution ccw EXIT BACKNEXT

13
270 radians ¾ revolution ccw EXIT BACKNEXT

14
360 2 radians one revolution ccw EXIT BACKNEXT

15
If one were to complete two revolutions ccw, what would this measure in radians? EXIT BACKNEXT

16
360 + 360 = 720 which is equivalent to 2 + 2 = 4 2 n gives the radian measurement for n complete counter-clockwise revolutions. EXIT BACKNEXT

17
What if we walked along the arc of a unit circle clockwise instead of counterclockwise? We simply insert a negative sign to indicate movement in the clockwise direction, as with degrees. EXIT BACKNEXT

18
Pictures to remember Revolve ccwRevolve cw m( ) = sm( ) = -s s = measure of arc length EXIT BACKNEXT

19
End of Radians Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA 91754 Phone: (323) 265-8784 Email Us At: menteprog@hotmail.com Our Website: http://www.matematicamente.org EXIT BACKNEXT

Similar presentations

OK

Concept. Example 1 Draw an Angle in Standard Position A. Draw an angle with a measure of 210° in standard position. 210° = 180° + 30° Draw the terminal.

Concept. Example 1 Draw an Angle in Standard Position A. Draw an angle with a measure of 210° in standard position. 210° = 180° + 30° Draw the terminal.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different types of computer softwares stores Ppt on polynomials in maths what does product Ppt on chromosomes and genes labeling Ppt on ufo and aliens today Cathode ray tube display ppt on tv Download ppt on areas of parallelograms and triangles Ppt on history of olympics in greece Ppt on social contract theory pdf Ppt on save energy save environment Ppt on children's day in india