This is a free lesson from our course in Trigonometry This lesson introduces and walks you through the ways to measure angles. Further a comparison of these methods i.e. degree and in radian will be shown with the help of video and explanation by the instructor in own hand writing. You'll also find some supporting examples and practice questions with solution. A degree is defined as 1/360 of a rotation of a radius about the center of a circle. Thus 360 = 1 complete rotation. A radian is the angle subtended at the center of a circle by an arc of the circle equal in length to its radius. Simply put, a circle is divided into 360 equal degrees, and a right angle (1/4th of the rotation) is 90 . The degrees range from 0 to 360 and radians range from 0 to 2 , where 2 is equivalent to 360 . (More text below video...)
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(Continued from above) Using the fact that 360 corresponds to 2 radians; we can generate the following angle measures:
• Dividing by 2 gives 180 which corresponds to .
• Dividing again by 2 gives 90 corresponds to /2.
• Dividing by 4 gives 45 which corresponding to /4.
Other radian measures of angle can be found for such angles as 150 or 240 or -135 , as these are multiples of 30 , 45 , and 60 . For example, since we know that 30 corresponds to /6 we can convert 150 to 5 /6 since 150 = 5(30 ).
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