AHL 3.7—Radians

To convert degrees to radians, multiply by $\frac{\pi }{180}$.

$315\times \frac{\pi }{180}=\frac{315\pi }{180}$.

$\frac{315}{180}=\frac{7}{4}$ since both divide by 45, giving $\frac{7\pi }{4}$.

$315°=\frac{7\pi }{4}$ radians.

$\frac{5\pi }{4}$ corresponds to $225°$, not $315°$.

$\frac{9\pi }{8}$ arises from an incorrect simplification of $\frac{315}{180}$, dividing by the wrong common factor.

$\frac{7\pi }{8}$ corresponds to $157.5°$, half of the correct angle, suggesting a doubling error was reversed incorrectly.

Only $\frac{7\pi }{4}$ correctly simplifies $\frac{315\pi }{180}$.

To convert radians to degrees, multiply by $\frac{180}{\pi }$.

$\frac{7\pi }{12}\times \frac{180}{\pi }=\frac{7\times 180}{12}$.

$\frac{1260}{12}=105$.

$\frac{7\pi }{12}$ radians equals $105°$.

$210°$ results from doubling the correct value, perhaps confusing $\frac{7\pi }{12}$ with $\frac{7\pi }{6}$.

$85°$ comes from an arithmetic slip when dividing $1260$ by $12$.

$120°$ would be the result of converting $\frac{2\pi }{3}$, not $\frac{7\pi }{12}$.

Only $105°$ matches the exact conversion.