The following tables contain identities and special triangle trig values that will be provided on the final exam should they be required.
| Name
|
Equation
|
| Law of Cosines
|
$a^2=b^2+c^2-2bc\cos(\theta)$
|
| Trig identities
|
$\sin^2\theta +\cos^2\theta=1$
|
|
|
$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$
|
|
|
$\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$
|
|
|
$\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$
|
| Special triangles
|
| $\theta$
|
$\sin(\theta)$
|
$\cos(\theta)$
|
| 0
|
0
|
1
|
| $\dfrac{\pi}{6}$
|
$\dfrac{1}{2}$
|
$\dfrac{\sqrt{3}}{2}$
|
| $\dfrac{\pi}{4}$
|
$\dfrac{\sqrt{2}}{2}$
|
$\dfrac{\sqrt{2}}{2}$
|
| $\dfrac{\pi}{3}$
|
$\dfrac{\sqrt{3}}{2}$
|
$\dfrac{1}{2}$
|
| $\dfrac{\pi}{2}$
|
1
|
0
|
| Geometric formulae (volume, area)
|
| Quantity
|
Formula
|
| Volume of sphere
|
$\dfrac{4}{3} \pi r^3$
|
| Surface area of sphere
|
$4\pi r^2$
|
| Volume of cone
|
$\dfrac{1}{3} \pi r^2h$
|
| Surface area of cone
|
$\pi r s$
|
|
|
|
