# Trig (Trigonometry) Formulas and Notes

Special Angles

 Degrees 0° 30° 45° 60° 90° Radians \displaystyle 0 \displaystyle \frac{ \pi}{6} \displaystyle \frac{ \pi}{4} \displaystyle \frac{ \pi}{3} \displaystyle \frac{ \pi}{2} sin(x) \displaystyle 0 \displaystyle \frac{1}{2} \displaystyle \frac{ \sqrt{2} }{2} \displaystyle \frac{ \sqrt{3} }{2} \displaystyle 1 cos(x) \displaystyle 1 \displaystyle \frac{ \sqrt{3} }{2} \displaystyle \frac{ \sqrt{2} }{2} \displaystyle \frac{ \sqrt{1} }{2} \displaystyle 0 tan(x) \displaystyle 0 \displaystyle \frac{ \sqrt{3} }{3} \displaystyle 1 \displaystyle \sqrt{3} -

Law of Sines and Cosines

Law of Sines

\displaystyle \frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}

Law of Cosines

\displaystyle a^2 = b^2+c^2-bc{\cos(A)}

\displaystyle b^2 = a^2+c^2-ac{\cos(B)}

\displaystyle c^2 = a^2+b^2-ab{\cos(C)}

Identities

\displaystyle \sin^2(\theta)+\cos^2(\theta) = 1

\displaystyle \sec(\theta) = \frac{1}{\cos(\theta)}

\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}

\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}

\displaystyle \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}

\displaystyle 1+\tan^2(\theta) = \sec^2(\theta)

\displaystyle 1+\cot^2(\theta) = \csc^2\theta

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

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

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

\displaystyle \csc(-\theta) = -\csc(\theta)

\displaystyle \sec(-\theta) = \sec(\theta)

\displaystyle \cot(-\theta) = -\cot(\theta)

\displaystyle \sin(a \pm b) = \sin(a)\cos(b) \pm \sin(b)\cos(a)

\displaystyle \cos(a \pm b) = \cos(a)\cos(b) \pm \sin(a)\sin(b)

\displaystyle \tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \pm \tan(a)\tan(b)}

\displaystyle \sin(2\theta) = 2\sin(\theta)\cos(\theta)

\displaystyle \cos(2\theta) = \cos^2\theta-\sin^2\theta

\displaystyle \cos(2\theta) = 1-2\sin^2(\theta)

\displaystyle \cos(2\theta) = 2\cos^2(\theta)-1

\displaystyle \tan(2\theta) = \frac{2\tan(\theta)}{1-\tan^2(\theta)}

\displaystyle \sin^2(\theta) = \frac{1-\cos(2\theta)}{2}

\displaystyle \cos^2(\theta) = \frac{1+\cos(2\theta)}{2}