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Tags: Trigonometry intro If one angle of a triangle is 90 degrees and one of the other angles is known the third is thereby fixed because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined except for similarity by the angles. Once the angles are known the ratios of the sides are determined regardless of the overall size of the triangle. If the length of one of the sides is known the other two are determined. These ratios are given by the following trigonometric functions of the known angle A where a b and c refer to the lengths of the sides in the accompanying figure: Sine function (sin) defined as the ratio of the side opposite the angle to the hypotenuse. Cosine function (cos) defined as the ratio of the adjacent leg (the side of the triangle joining the angle to the right angle) to the hypotenuse. Tangent function (tan) defined as the ratio of the opposite leg to the adjacent leg. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg' is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively.(see below under Mnemonics). The reciprocals of these functions are named the cosecant (csc) secant (sec) and cotangent (cot) respectively: The inverse functions are called the arcsine arccosine and arctangent respectively. There are arithmetic relations between these functions which are known as trigonometric identities. The cosine cotangent and cosecant are so named because they are respectively the sine tangent and secant of the complementary angle abbreviated to "co-". With these functions one can answer virtually all q


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