Radians of the unit circle.

**Eraser147** · November 2nd 2012, 09:21 AM

For the radians of the unit circle that are degree 30, 45, and 60.. is there a way where I can find the radians without using a calculator by converting degree to radians? Like for example why is 60 degrees on the unit circle pi over 3. What is the formula for adding up the radians throughout the whole unit circle?

**HallsofIvy** · November 2nd 2012, 09:50 AM

You just need to know: 1) the relation ship is linear, 2) 0 degrees= 0 radians, 3) 360 degrees= $2\pi$ radians
$\frac{x degrees}{y radians}= \frac{360}{2\pi}$ .

So if "x degrees" is "30 degrees" we have $\frac{30 degrees}{y radians}= \frac{360}{2\pi}$ . Now "cross multiply": $(y radians)(360)= (30 degrees)(2\pi)= 60\pi$ . $y radians= \frac{60\pi}{360}= \frac{\pi}{6} radians$ .

**Plato** · November 2nd 2012, 09:56 AM

Originally Posted by Eraser147

For the radians of the unit circle that are degree 30, 45, and 60.. is there a way where I can find the radians without using a calculator by converting degree to radians? Like for example why is 60 degrees on the unit circle pi over 3. What is the formula for adding up the radians throughout the whole unit circle?

Think in terms of units, like feet, yards, meters etc.
$(N\deg)\left(\frac{\pi}{180\deg}\right)=\left( \frac{N\pi}{180}\right)$

$(N^o)\left(\frac{\pi}{180^o}\right)=\left( \frac{3\pi}{4}\right)$

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