Understanding Radians: Essential for Engineers, Scientists, and Mathematicians

1. What professionals might use radians? Any engineer or scientist who deals with electricity, someone who works with electronic music, automotive engineers, electronic circuit designers, and my favorite, mathematicians.

2. So What is a Radian, Really? • Locate the center of a circle by balancing the circle on the tip of a pencil. • Mark the length of the radius of the circle on an index card. Cut the card the length of the radius • Create a radius wedge (a pie-shaped piece formed by two radii and an arc length of 1 radius) • Measure the angle in degrees. 1 radian is approximately _______ degrees. • Continue marking full radians around the circle. Approximately how many radians are there in a full circle? _______ • How many in a half circle? _______ • The formula for the circumference of a circle is _____________. The radius of our circle is one, so the number of radians in a 360˚ circle is _________. • The number of radians in a semicircle (180˚) is _____________. • The number of radians in a quarter circle is (90˚) is ______________. • The number of radians in an eighth circle is (45˚) is ______________.

3. Radian The measure of is “s” radians. A more convenient method for measuring angles (instead of degrees) in upper level mathematical applications. The radian measure of an angle in standard position is defined as the length of the corresponding arc on the unit circle.

4. FYI (On the Calculator):

5. Degrees to radians: multiply by π/180 Radians to degrees: multiply by 180/π It will be helpful to memorize these common angle measures and their equivalent radian measures:

6. 60° 1 Remember “The Chart” 240˚ is in Quadrant III, so the sign is . . . All Students Take Calculus - 1/2 . . . negative

9. Sector – the region bounded by a central angle and its intercepted arc

10. Example 6

11. HW: Page 348