From Degrees to RadiansDate: 09/22/98 at 18:31:19 From: Little Fairy Subject: Radians Nine degrees equals how many radians? How do you solve problems like this? What are radians? Date: 09/22/98 at 18:45:28 From: Doctor Pat Subject: Re: Radians If you make an angle at the center of a circle and extend it out until the two rays of the angle cut the circle, the angle can be measured in two ways. The first would be the degree measure that you know of; the second would be to use the length of the arc of circle between the two rays of the angle. Notice that if we do this, the measurement will be different for different-size circles. This is not true for degree measure of angles. To correct for the different sizes of circles, the arc length is divided by the length of a radius of the circle, and this measurement is called radians. An angle that has a measure of 1 radian would cut an arc equal to the length of 1 radius of whatever size circle you drew (try it). Since we know it takes 2*pi radii to reach around a circle (circumference = 2*pi*r), and that a circle has 360 degrees, we can use this relation to convert between degrees and radians. To convert 9 degrees to radians we set up a proportion like this: 9 ? ----- = ----- 360 2*pi and solve. In this case 18*pi/360 is the answer, but you might want to make that a decimal or reduce the fraction. I hope this helps a little. You may find some more information at David Joyce's "A short course in trigonometry." Look at number 4: Angle measurement. http://aleph0.clarku.edu/~djoyce/java/trig/ - Doctor Pat, The Math Forum http://mathforum.org/dr.math/ |
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