Theory of Horology

Theory of Horology


Section 5 Mathematical Formulas

5-1 Trigonometric Function

5-1-6 Half-angle Formula

$sin\frac{\theta}{2}=\pm\sqrt{\frac{1-cos\theta}{2}}$$cos\frac{\theta}{2}=\pm\sqrt{\frac{1+cos\theta}{2}}$$tan\frac{\theta}{2}=\pm\sqrt{\frac{1-cos\theta}{1+cos\theta}}$
$ $$ $$\;\;\;\;\;\;\;\;\;\;=\frac{sin\theta}{1+cos\theta}$
$ $$ $$\;\;\;\;\;\;\;\;\;\;=\frac{1-cos\theta}{sin\theta}$