Difference between revisions of "Trigonometry"

Revision as of 20:58, 23 June 2006

Trigonometry seeks to find the lengths of a triangle's sides, given 2 angles and a side. Trigonometry is closely related to analytic geometry.

Basic definitions

Usually we call an angle $\displaystyle \theta$ , read "theta", but $\theta$ is just a variable. We could just as well call it $a$ .

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Sine

The sine of an angle $\theta$ , abbreviated $\displaystyle \sin \theta$ , is the ratio between the base and the hypotenuse of a triangle with the uppermost angle equal to theta. For instance, in the 30-60-90 triangle above, $\sin 30=\frac 12$ .

Cosine

The cosine of an angle $\theta$ , abbreviated $\displaystyle \cos \theta$ , is the ratio between the altitude and the hypotenuse of a triangle with the uppermost angle equal to theta. For instance, in the 30-60-90 triangle above, $\cos 30=\frac{\sqrt{3}}{2}$ .

Tangent

The tangent of an angle $\theta$ , abbreviated $\displaystyle \tan \theta$ , is the ratio between the base and altitude of a triangle with the uppermost angle equal to theta. For instance, in the 30-60-90 triangle above, $\tan 30=\frac{1}{\sqrt{3}}$ . (Note that $\tan \theta=\frac{\sin\theta}{\cos\theta}$ .)

@@ Line 13: / Line 13: @@
 ===[[Tangent]]===
-The tangent of an angle <math>\theta</math>, abbreviated <math>\tan \theta</math>, is the ratio between the base and altitude of a triangle with the uppermost angle equal to [[theta]]. For instance, in the 30-60-90 triangle above, <math>\tan 30=\frac{1}{\sqrt{3}}</math>. (Note that <math> \tan \theta=\frac{\sin\theta}{\cos\theta}</math>.)
+The tangent of an angle <math>\theta</math>, abbreviated <math>\displaystyle \tan \theta</math>, is the ratio between the base and altitude of a triangle with the uppermost angle equal to [[theta]]. For instance, in the 30-60-90 triangle above, <math>\tan 30=\frac{1}{\sqrt{3}}</math>. (Note that <math> \tan \theta=\frac{\sin\theta}{\cos\theta}</math>.)
 ==See also==

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