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 (1/4^{th} of the rotation) is 90.
The degrees range from 0
to 360
and radians range from 0 to 2,
where 2is equivalent
to 360. (More text below video...)
(Continued from above) Using the fact that 360corresponds
to 2
radians; we can generate the following angle measures:
Dividing by 2 gives 180which
corresponds to
.
Dividing again by 2 gives 90
corresponds to
/2.
Dividing by 4 gives 45which
corresponding to
/4.
Other radian measures of angle can be found for such angles as 150or
240or 135,
as these are multiples of 30,
45, and 60.
For example, since we know that 30corresponds
to
/6 we can convert 150to 5/6
since 150
= 5(30).
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