151116 初版 151116 更新
例
\(\sin\left(\theta+\dfrac{\pi}{4}\right)=\dfrac{1}{2}\) を満たす θ
一般には，
\(\theta+\dfrac{\pi}{4} = \dfrac{\pi}{6}+2n\pi\),
\(\dfrac{5}{6}\pi+2n\pi\)
(n は整数)
すなわち，
\(\theta = \dfrac{-1+24n}{12}\pi\),
\(\dfrac{7+24n}{12}\pi\)
(n は整数)
0 ≦ θ < 2π では，
\(\theta = \dfrac{7}{12}\pi\),
\(\dfrac{23}{12}\pi\)
例
\(\sin\left(\theta+\dfrac{\pi}{4}\right) >\dfrac{1}{2}\) を満たす
θ
一般には，
\(\dfrac{\pi}{6}+2n\pi < \theta+\dfrac{\pi}{4}\)
\(< \dfrac{5}{6}\pi+2n\pi\)
(n は整数)
すなわち，
\(\dfrac{-1+24n}{12}\pi < \theta\)
\(< \dfrac{7+24n}{12}\pi\)
(n は整数)
0 ≦ θ < 2π では，
\(0\leqq \theta < \dfrac{7}{12}\pi\),
\(\dfrac{23}{12}\pi < \theta < 2\pi\)
例
\(\sin\left(\theta+\dfrac{\pi}{4}\right) <\dfrac{1}{2}\) を満たす θ
一般には，
\(\dfrac{5}{6}\pi+2n\pi < \theta+\dfrac{\pi}{4}\)
\(< \dfrac{13}{6}\pi+2n\pi\)
(n は整数)
すなわち，
\(\dfrac{7+24n}{12}\pi < \theta\)
\(< \dfrac{23+24n}{12}\pi\)
(n は整数)
0 ≦ θ < 2π では，
\(\dfrac{7}{12}\pi < \theta\)
\(< \dfrac{23}{12}\pi\)