三角関数の性質、周期性 理解補助ツール

基本の定義

\( \sin\theta = y \)

\( \cos\theta = x \)

\( \tan\theta = \frac{y}{x} \)

-θ の公式 (x軸対称)

\( \sin(-\theta) = -\sin\theta \)

\( \cos(-\theta) = \cos\theta \)

\( \tan(-\theta) = -\tan\theta \)

θ+π の公式 (原点対称)

\( \sin(\theta+\pi) = -\sin\theta \)

\( \cos(\theta+\pi) = -\cos\theta \)

\( \tan(\theta+\pi) = \tan\theta \)

θ+π/2 の公式 (90°回転)

\( \sin(\theta+\frac{\pi}{2}) = \cos\theta \)

\( \cos(\theta+\frac{\pi}{2}) = -\sin\theta \)

\( \tan(\theta+\frac{\pi}{2}) = -\frac{1}{\tan\theta} \)

π-θ の公式 (y軸対称)

\( \sin(\pi-\theta) = \sin\theta \)

\( \cos(\pi-\theta) = -\cos\theta \)

\( \tan(\pi-\theta) = -\tan\theta \)

\( P(\cos\theta, \sin\theta) \)

\( \tan\theta \)

\( \theta \)

\( Q(\cos(-\theta), \sin(-\theta)) \)

\( \tan(-\theta) \)

\( -\theta \)

\( Q(\cos(\theta+\pi), \sin(\theta+\pi)) \)

\( \tan(\theta+\pi) \)

\( \theta+\pi \)

\( Q(\cos(\theta+\frac{\pi}{2}), \sin(\theta+\frac{\pi}{2})) \)

\( \tan(\theta+\frac{\pi}{2}) \)

\( \theta+\frac{\pi}{2} \)

\( Q(\cos(\pi-\theta), \sin(\pi-\theta)) \)

\( \tan(\pi-\theta) \)

\( \pi-\theta \)

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