Difference between revisions of "Final exam information"
From UBCMATH WIKI
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{|style="border-collapse: collapse;" class="withlines" | {|style="border-collapse: collapse;" class="withlines" | ||
− | + | !style="width: 200px;"|Trig identity | |
− | !style="width: 200px;"| | + | |
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|$a^2=b^2+c^2-2bc\cos(\theta)$ | |$a^2=b^2+c^2-2bc\cos(\theta)$ | ||
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|$\sin^2\theta +\cos^2\theta=1$ | |$\sin^2\theta +\cos^2\theta=1$ | ||
|- | |- | ||
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|$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$ | |$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$ | ||
|- | |- | ||
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|$\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$ | |$\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$ | ||
|- | |- | ||
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|$\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$ | |$\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$ | ||
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Revision as of 13:39, 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.
Trig identity |
---|
$a^2=b^2+c^2-2bc\cos(\theta)$ |
$\sin^2\theta +\cos^2\theta=1$ |
$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$ |
$\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$ |
$\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$ |
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 | $\pi r s$ | |