【高校数学Ⅱ】4-1-1 一般角と弧度法｜問題集

\(500°=140°+360°\times1\)
よって、
\(140°\)で第\(2\)象限にある。

\(-100°=260°+360°\times(-1)\)
よって、
\(260°\)で第\(3\)象限にある。

\(800°=80°+360°\times2\)
よって、
\(80°\)で第\(1\)象限にある。

\(-200°=160°+360°\times(-1)\)
よって、
\(160°\)で第\(2\)象限にある。

\(\displaystyle 30°\times\frac{\pi}{180}=\frac{1}{6}\pi\)

\(\displaystyle 225°\times\frac{\pi}{180}=\frac{5}{4}\pi\)

\(\displaystyle 60°\times\frac{\pi}{180}=\frac{1}{3}\pi\)

\(\displaystyle -210°\times\frac{\pi}{180}=-\frac{7}{6}\pi\)

\(\displaystyle 135°\times\frac{\pi}{180}=\frac{3}{4}\pi\)

\(\displaystyle -108°\times\frac{\pi}{180}=-\frac{3}{5}\pi\)

\(\displaystyle 123°\times\frac{\pi}{180}=\frac{41}{60}\pi\)

\(\displaystyle \frac{4}{3}\pi\times\frac{180}{\pi}=240°\)

\(\displaystyle \frac{\pi}{60}\times\frac{180}{\pi}=3°\)

\(\displaystyle \frac{\pi}{4}\times\frac{180}{\pi}=45°\)

\(\displaystyle -\frac{7}{20}\pi\times\frac{180}{\pi}=-63°\)

\(\displaystyle \frac{\pi}{2}\times\frac{180}{\pi}=90°\)

\(\displaystyle -\frac{13}{10}\pi\times\frac{180}{\pi}=-234°\)

\(\displaystyle l=4\times\frac{\pi}{3}=\frac{4}{3}\pi\)
\(\displaystyle S=\frac{1}{2}\times4^2\times\frac{\pi}{3}=\frac{8}{3}\pi\)

\(\displaystyle l=6\times\frac{7}{6}\pi=7\pi\)
\(\displaystyle S=\frac{1}{2}\times6^2\times\frac{7}{6}\pi=21\pi\)

\(\displaystyle l=10\times\frac{2}{5}\pi=4\pi\)
\(\displaystyle S=\frac{1}{2}\times10^2\times\frac{2}{5}\pi=20\pi\)

\(\displaystyle l=9\times\frac{2}{3}\pi=6\pi\)
\(\displaystyle S=\frac{1}{2}\times9^2\times\frac{2}{3}\pi=27\pi\)