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By definition, the number of radians in one complete revolution is given by the ratio of the circumference of a circle to its radius.
The circumference of a circle of radius r is of length 2πr.
There are thus 2πr/r = 2π radians in one revolution.
So, 2π radians = 360°
Then 1 radian = 360/2π = 57.296° or 57° 17'
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If a circle is divided into 360 equal parts what is the degree measure of the 360 angles?
A circle is divided into 360° and each of them is 1° ■
Is a degree one of 360 equal-sized parts of a circle?
Yes, that is one kind of degree.
Why multiply degree to pi by 180 to convert it to radian?
A whole circle is 360 degrees or 2*pi radians. 360 degrees = 2*pi radians so that 1 degree = pi/180 radians This gives the conversion factor of pi/180 to convert degrees to radians.
What is a degree measure?
It is an old convention where everything is perfect like a circle, and each year have 360 days (for some reason). The ancients decided to make the unit to measure angles using this system, defining the angle of a full rotation is the godly number 360, and then split down. Now, a more useful and intuitive definition is given, called a radian measure. Where the radian measure of a full rotation as the circumference of the UNIT CIRCLE (circle with radius 1), which is 2 pi.
How many arc minutes in a full circle?
There are 60 arcminutes in one degree. There are 360 degrees in a circle. Therefore, one full rotation is equal to 360 x 60 = 21600 arcminutes.
