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Miike012
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Homework Statement
What made them pick one rad equal to 57 deg.
Why didn't the pick 45 deg. or 90 deg. or any other random degree to equal one rad.?
The value of 57 degrees for one radian is based on the definition of a radian, which is the measure of an angle that subtends an arc equal in length to the radius of a circle. Since the circumference of a circle is 2π times the radius, it follows that there are 2π radians in a full circle. Using simple algebra, we can calculate that 360 degrees (a full circle) is equivalent to 2π radians, which gives us the conversion factor of 180/π, or approximately 57.3 degrees per radian.
The value of 57 degrees for one radian has historical roots dating back to ancient civilizations. The Babylonians used a base-60 number system and divided the circle into 360 degrees, while the Ancient Greeks divided the circle into 360 parts for mathematical convenience. However, the concept of radians was introduced by the mathematician Roger Cotes in the 18th century, who chose the value of 57 degrees based on the properties of circles and trigonometry.
The value of 57 degrees for one radian is a close approximation of the actual value, which is 180/π or approximately 57.2958 degrees. This slight difference is negligible in most calculations and using 57 degrees makes it easier to convert between radians and degrees in mathematical equations.
The value of 57 degrees for one radian is a fundamental constant in mathematics and is not subject to change. It has been widely accepted and used for centuries, and any changes would result in significant disruptions in mathematical calculations and formulas.
The value of 57 degrees for one radian is crucial in trigonometry, as it allows for easy conversion between radians and degrees. It also plays a significant role in calculus, where radians are used to measure angles in polar coordinates. Additionally, the value of 57 degrees for one radian affects many other mathematical concepts, such as the unit circle, trigonometric identities, and the graphing of trigonometric functions.