Difference between revisions of "Tangent"
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(At their point of intersection, the curve and the line have exactly the same slope) |
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<math>\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \,</math> | <math>\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \,</math> | ||
| − | In [[analytic geometry]], a line which | + | In [[analytic geometry]], a line which intersects a [[circle]] or [[curve]] at only one point is said to be tangent to that circle or curve. At the point of intersection, the curve and the line have exactly the same [[slope]]. |
Compare: [[Asymptote]] | Compare: [[Asymptote]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 19:17, November 15, 2007
In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the opposite and adjacent sides.
We can also see a relationship between the sine and cosine functions:
<math>\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \,</math>
In analytic geometry, a line which intersects a circle or curve at only one point is said to be tangent to that circle or curve. At the point of intersection, the curve and the line have exactly the same slope.
Compare: Asymptote