Question

Which expression converts 45° to radians? 45 degrees times 180 degrees 45 degrees times StartFraction 180 degrees Over pi EndFraction 45 degrees times StartFraction pi Over 180 degrees EndFraction 45 degrees times pi.

Answer 1

One short cut to remember how the solution is found, remember that degree unit must be removed and radian has to come(to convert from degree to radian) and that will be removed only when division by degree will happen and multiplication by something in radian.

The correct expression that converts 45° to radian is given by:
Option C:  $45^\circ \times \dfrac{\pi^c}{180^\circ}$

How is degree related to radian?

Both measure angles. Remember the fact that one full rotation is 360° or $2\pi^c$ (this superscript c denotes that angle is in radians).

pi is 3.14159... and pi radians means 3.14.. radians which measures half of full rotation(since 2 times pi measures full rotation).

Thus, we have:

$360^\circ = 2\pi^c\\\\ \text{Dividing by 360 on both sides}\\\\ 1^\circ = \dfrac{2\pi^c}{360}\\\\ 1^\circ = \dfrac{\pi^c}{180}$

Thus, we have:

$45^\circ = 45 \times 1^\circ = 45 \dfrac{\pi^c}{180} = \dfrac{45^\circ\pi^c}{180^\circ}$

Thus, the correct expression that converts 45° to radian is given by:
Option C:  $45^\circ \times \dfrac{\pi^c}{180^\circ}$

Learn more about degree and radian here:

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