Theory of Horology

Theory of Horology


Section 5 Mathematical Formulas

5-1 Trigonometric Function

5-1-2 Symmetric Property

Symmetric with respect to $\theta=0$(x-axis)Symmetric with respect to $\theta=\pi/4$Symmetric with respect to $\theta=\pi/2$(y-axis)
$sin(-\theta)=-sin\theta$$sin(\frac{\pi}{2}-\theta)=+cos\theta$ $sin(\pi-\theta)=+sin\theta$
$cos(-\theta)=+cos\theta$$cos(\frac{\pi}{2}-\theta)=+sin\theta$$cos(\pi-\theta)=-cos\theta$
$tan(-\theta)=-tan\theta$$tan(\frac{\pi}{2}-\theta)=+cot\theta$$tan(\pi-\theta)=-tan\theta$