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if is equal to , what is the value of ? (The number of degrees of arc in a circle is . The number of radians of arc in a circle is .)
Full solution
Q. if is equal to , what is the value of ? (The number of degrees of arc in a circle is . The number of radians of arc in a circle is .)
- Relationship between radians and pi: Understand the relationship between radians and pi.The problem states that is equal to . In mathematics, pi () is a constant that represents the ratio of the circumference of a circle to its diameter, and it is approximately equal to . When dealing with angles, radians is equivalent to degrees. Therefore, to find the value of in radians, we simply need to consider the value given for .
- Calculate in radians: Calculate the value of in radians.Since is given as , we do not need to perform any calculations to find the value of in radians. The value of is already given in terms of , which is the standard unit for measuring angles in radians.
- Confirm unit of : Confirm that the value of is in the correct unit.The problem does not ask for the conversion of into degrees or any other unit. It simply asks for the value of , which is given as . Since is a unit for radians, and there is no request for conversion, we can conclude that the value of is radians.
