Trigonometry

• Radians to degrees conversion:

  $2\pi=$ 360

  $\pi=$ 180

  $\frac{\pi}{2}$ = 90

  $\frac{\pi}{3}=$ 60

  $\frac{\pi}{4}=$ 45

  $\frac{\pi}{6}=$ 30
• Small angle approximations

  $\sin\theta\approx$ $\theta$

  $\cos\theta\approx$ $1-\frac{\theta^2}{2}$

  $\tan\theta\approx$ $\theta$
• Exact sine trig values

  $\sin30=$ $\frac{1}{2}$

  $\sin60=$ $\frac{\sqrt{3}}{2}$

  $\sin45=$ $\frac{1}{\sqrt{2}}$
• Tangent defnition

  $\tan\theta=$ $\frac{\sin\theta}{\cos\theta}$
• Solving equations

  $\sin\theta=$ $\sin\left(180-\theta\right)$ $\pm360\degree$

  $\cos\theta=$ $\cos\left(360-\theta\right)$ $\pm360\degree$

  $\tan\theta=$ $\tan\left(180+\theta\ \right)$ $\pm180\degree$
• Reciprocal trig functions

  $\operatorname{cosec}\theta=$ $\frac{1}{\sin\theta}$

  $\sec\theta=$ $\frac{1}{\cos\theta}$

  $\cot\theta=$ $\frac{1}{\tan\theta}$
• Co-functions

  $\sin\theta=$ $\cos\left(90-\theta\right)$

  $\cos\theta=$ $\sin\left(90-\theta\right)$
• Pythagorean identities

  $\sin^2\theta+$$\cos^2\theta=$ $1$

  $1+$$\tan^2\theta=$ $\sec^2\theta$

  $1+$$\cot^2\theta=$ $\operatorname{cosec}^2\theta$
• Double angle formulae

  $\sin2\theta=$ $2\sin\theta\cos\theta$

  $\cos2\theta=$ $\cos^2\theta-\sin^2\theta$

  $\cos2\theta=$ $2\cos^2\theta-1$

  $\cos2\theta=$ $1-2\sin^2\theta$

  $\tan2\theta=$ $\frac{2\tan\theta}{1-\tan^2\theta}$
• Addition formulae

  $\sin\left(A\pm B\right)=$ $\sin A\cos B\pm\cos A\sin B$

  $\cos\left(A\pm B\right)=$ $\cos A\cos B\mp\sin A\sin B$

  $\tan\left(A\pm B\right)=$ $\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}$