From Förberedande kurs i matematik 1

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

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

this gives

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

Now we can start transforming the angles:

a) \displaystyle 45^{\circ }=45\centerdot 1^{\circ }=45\centerdot \frac{\pi }{180} radians \displaystyle =\frac{\pi }{4} radians

b) \displaystyle 135^{\circ }=135\centerdot 1^{\circ }=135\centerdot \frac{\pi }{180} radians \displaystyle =\frac{3\pi }{4} radians

c) \displaystyle -63^{\circ }=-63\centerdot 1^{\circ }=-63\centerdot \frac{\pi }{180} radians \displaystyle =-\frac{7\pi }{20} radians

d) \displaystyle 270^{\circ }=270\centerdot 1^{\circ }=270\centerdot \frac{\pi }{180} radians \displaystyle =\frac{3\pi }{2} radians