Aus Online Mathematik Brückenkurs 1

If we use the mnemonic that one turn is 360° or \displaystyle 2\pi radians, we can derive a formula for the transformation from degrees to radians. Because

\displaystyle 360\cdot 1^{\circ } = 2\pi\ \text{radians}

this gives

\displaystyle 1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}

Now we can start transforming the angles:

a)	\displaystyle 45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,}
b)	\displaystyle 135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}
c)	\displaystyle -63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,}
d)	\displaystyle 270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.}