Difference between revisions of "Final exam information"
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| + | !colspan=3|Geometric formulae (volume, area) | ||
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| + | !style="width: 70px;"|Quantity | ||
| + | !style="width: 70px;"|Formula | ||
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| + | |Volume of sphere | ||
| + | |$\dfrac{4}{3} \pi r^3$ | ||
| + | |- | ||
| + | |Surface area of sphere | ||
| + | |$4\pi r^2$ | ||
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| + | |Volume of cone | ||
| + | |$\dfrac{1}{3} \pi r^2h$ | ||
| + | |- | ||
| + | |Surface area of cone | ||
| + | |$\pi r s$ | ||
| + | |- | ||
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Revision as of 13:32, 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 | $\pi r s$ | |
