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There is more than one equivalent definition. One way to think of this is this:

Imagine a right triangle, with an angle "x". The sides of the triangles are as follow: side "a" is opposite to the angle "x", side "b" is adjacent to the angle, and side "c" is the hypothenuse (the longest side, opposite the right angle). In this case:

* sin(x) = a/c

* cos(x) = b/c

* tan(x) = a/b = sin(x) / cos(x)

* cot(x) = b/a = cos(x) / sin(x)

* csc(x) = c/a = 1 / sin(x)

* sec(x) = c/b = 1 / cos(x)

These ratios of sides will depend on the angle "x", but for any angle "x", the ratio will always be the same. For example, for an angle of 30°, the ratio a/c (sine of x) will always be 1/2.

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