Difference between revisions of "Final exam information"
From UBCMATH WIKI
| Line 53: | Line 53: | ||
!colspan=3|Geometric formulae (volume, area) | !colspan=3|Geometric formulae (volume, area) | ||
|- | |- | ||
| − | !style="width: | + | !style="width: 150px;"|Quantity |
| − | !style="width: | + | !style="width: 150px;"|Formula |
|- | |- | ||
|Volume of sphere | |Volume of sphere | ||
Revision as of 13:37, 20 November 2013
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 | $\pi r s$ | |
