Trigonometry

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 $\tan \theta$ , 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 $\tan \theta=\frac{\sin\theta}{\cos\theta}$ .)

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Trigonometry

Contents

Basic definitions

Sine

Cosine

Tangent

See also