Theory of Horology

Theory of Horology


Section 5 Mathematical Formulas

5-1 Trigonometric Function

5-1-5 Double-angle Formula

$sin2\theta=2sin\theta \;cos\theta$$cos2\theta=cos^2\theta-sin^2\theta$$tan2\theta=\frac{2tan\theta}{1-tan^2\theta}$
$\;\;\;\;\;\;\;\;\;\;=\frac{2tan\theta}{1+tan^2\theta}$$\;\;\;\;\;\;\;\;\;\;=2cos^2\theta-1$ $ $
$ $$\;\;\;\;\;\;\;\;\;\;=1-2sin^2\theta$$ $
$ $$\;\;\;\;\;\;\;\;\;\;=\frac{1-tan^2\theta}{1+tan^2\theta}$$ $