In this lesson, we will learn
We can define radian in terms of the arc length and the radius:
The size of an angle in radian is given by the ratio of the arc length to the length of the radius.
An angle with 1 radian will have an arc length that is equal to the length of the radius.
An angle with 2 radians will have an arc length that is twice the length of the radius.
We can also define radian in terms of the unit circle (a circle of radius 1).
Consider the unit circle whose center is the vertex of the angle to be measured. The angle cuts off an arc of the circle, and the length of that arc is the radian measure of the angle.How to define radian in terms of the unit circle?
We can convert between degree measurement and radian measurement easily.
We know that the circumference of a circle is 2πr. For a unit circle, r = 1 and so the circumference = 2π
This means that 360° equals 2π radians.
Therefore, 1° = radians, and 1 radian = degrees.
The following are some common angles in both degree measurement and radian measurement.
Worksheet to convert between radians and degrees
A circle is divided into 360 equal degrees. Degrees may be further divided into minutes and seconds. Each degree is divided into 60 equal parts called minutes. Each minute is further divided into 60 equal parts called seconds.
1° (degree) = 60' (minutes)
1' (minute) = 60'' (seconds)
For example, 34 degrees 26 minutes 51 seconds can be written as 34° 26’ 51’’
Parts of a degree can also be written in decimal notation.
For example, 60 degrees 30 minutes is 60 and a half degrees which can be written as 60.5°
Convert 52.4˚ to degrees and minutes.
52.4˚ = 52˚ + 0.4˚
= 52˚ + (0.4 × 60)’
= 52˚ 24’
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