Q:

# What are the meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

A:

The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.

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In trigonometry, the three sides of a right triangle are identified as the hypotenuse, the side opposite the selected angle, and the side adjacent to the selected angle. Each of the trigonometric functions relates the measure of the selected angle to one of three ratios involving the lengths of the sides. The sine of an angle is equal to the length of the side opposite the angle over the length of the hypotenuse. The cosine of an angle is equal to the length of the adjacent side over the length of the hypotenuse. The tangent of an angle is equal to the length of the opposite side over the adjacent side. The trigonometric values for an angle of a certain measure are always the same, and they can be found in a trigonometric table. The other three functions, cosecant, secant and cotangent, are the reciprocal functions of the sine, cosine and cotangent, respectively. The cosecant of an angle equals 1/sine, the secant equals 1/cosine and the cotangent equals 1/tangent.

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