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 , read "theta", but is just a variable. We could just as well call it .
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Sine
The sine of an angle , abbreviated , 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, .
Cosine
The cosine of an angle , abbreviated , 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, .
Tangent
The tangent of an angle , abbreviated , 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, . (Note that .)