A radian is a unit of an angle, equal to an angle at the center of a circle whose arc is equal in length to the radius. Radians make math easier because they are an exact measurement of an angle. To explain to radians to someone who has never heard of them, a comparison between degrees and radians should be made. Degrees measure how we far tilt our heads, radians measure how far we travel.
Radians have special relationships with arc lengths in a unit circle. The size of a radian is determined by the requirement that there are 2pi radians in a circle. Thus 2pi radians equals 360 degrees. This means that 1pi radian = 180/pi degrees, and 1 degree =pi /180 radians. The formula for the circumference of a circle is 2(pi)r and there are 2pi in a circle.
It is easier to subtract, add, multiply, and divide using degrees but radians are more accurate and pure so answers should be in radians.
Radians have special relationships with arc lengths in a unit circle. The size of a radian is determined by the requirement that there are 2pi radians in a circle. Thus 2pi radians equals 360 degrees. This means that 1pi radian = 180/pi degrees, and 1 degree =pi /180 radians. The formula for the circumference of a circle is 2(pi)r and there are 2pi in a circle.
It is easier to subtract, add, multiply, and divide using degrees but radians are more accurate and pure so answers should be in radians.