From Förberedande kurs i matematik 1

The only thing we really need to remember is that one turn corresponds to \displaystyle \text{36}0^{\text{o}} or \displaystyle \text{2}\pi radians. Then we get:

a) \displaystyle \frac{1}{4} turn \displaystyle =\frac{1}{4}\centerdot 360^{\circ }=90^{\circ } and

\displaystyle \frac{1}{4} turn \displaystyle =\frac{1}{4}\centerdot 2\pi radians \displaystyle =\frac{\pi }{2} radians,

b) \displaystyle \frac{3}{8} turn \displaystyle =\frac{3}{8}\centerdot 360^{\circ }=135^{\circ } and

\displaystyle \frac{3}{8} turn \displaystyle =\frac{3}{8}\centerdot 2\pi radians \displaystyle =\frac{3\pi }{4} radians,

c) \displaystyle -\frac{2}{3} turn \displaystyle =-\frac{2}{3}\centerdot 360^{\circ }=-240^{\circ } and

\displaystyle -\frac{2}{3} turn \displaystyle =-\frac{2}{3}\centerdot 2\pi radians \displaystyle =-\frac{4\pi }{3} radians,

d) \displaystyle \frac{97}{12} turn \displaystyle =\frac{97}{12}\centerdot 360^{\circ }=2910^{\circ } and

\displaystyle \frac{97}{12} turn \displaystyle =\frac{97}{12}\centerdot 2\pi radians \displaystyle =\frac{97\pi }{6} radians,