ANGLES, DEGREE AND RADIAN

The earth circles the sun in 365 days. So the ancient people devided the circle into 360 degree. And 360 is also the base of 60. Hence they felt comfortable. We use this concept even today. But there is more convenient unit called Radian. Imagine the circle of unit radius.
Here
circumference = c= 2*pi*r=2*pi.*1 =2*pi
c= 2*3.14 = 6.28
Hence, we can say, the total angle of the circle 360 degree(full circle) is proportional to 2pi. or 180 degree(half circle) is proportional to pi. 90 degree(quarter circle) is proportional to pi/2.

Hence we can measure the angle in terms of pi. That is, we can measure the angle in terms of arc length in unit circle.This unit is called radian.

360 degree in radian is 2pi=2*3.14 =6.28....
hence 1 degree in radian is 0.0175 radian.

There are some advantages in this unit.

1.Suppose you want to know the length of arc held by the angle T radian in the circle of radius R, you simply find R*T, you get the arc.
Logic: T is the arc in unit circle for the angle T radian. If you find R*T, the arc is scaled to the circle of radius R.

2. Suppose you want to find the speed of a car. The car's wheel makes 10.5 rotations per second. Or it makes 10*2pi radians (angle) in one second. Multiply 20*pi by the radius of the wheel, you get the length traveled by the wheel in one second or the velocity of the car.

3. If the angle X measured in radian is very small then,
sin(x) =x
Radian makes the calculation easy.

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