Question

What is `(7pi)/12` radians in degrees?

Answer 1

`105^@`

Explanation:

If one revolution is `2pi` radians, and it is also `360^@`, we can make a conversion factor:

`(7cancel(pi))/12 cancel("rad")*(360^@)/(2cancel(pi) cancel("rad"))`

This lets us cancel out the pi's and the radians, to give us just degrees. Now, we can reduce the fraction as much as possible before completing the conversion:

`7/12*360^@/2 rArr 7/12*180^@`

`7*180^@/12 rArr 7*15^@ = 105^@`