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1 VIII_OLYMPIAD_PHYSICS_VOL-1 MATHEMATICS FOR PHYSICS TRIGONOMETRY SYNOPSIS Introduction: The word ‘trigonometry’ is derived from the Greek roots --- ‘tri’ meaning ‘three’; ‘gonia’ meaning ‘an angle’ ; ‘metron’ meaning ‘measure’. Thus ‘trigonometry’ means three angle measure. It is an analytical study of a three angled geometric figure, namely the triangle. Trigonometrical Ratios:In right triangle OPM, if  POM =  , then the side MP (perpendicular) is called the opposite side ; the longest side OP is called the hypotenuse and the third side OM is called the Adjacent side (base) of the triangle. P X O M X I Y YI  P X O M X I Y YI  (i) Sine of angle  , written as sin  = MP OP = Opposite side Hypotenuse side (ii) Cosine of angle  , written as cos  = OM OP = Adjacent side Hypotenuse side (iii) Tangent of angle  , written as tan  = MP OM = Opposite side Adjacent side (iv) Cotagent of angle  , written as cot  = OM MP = Adjacent side Opposite side (v) Secant of angle  , written as sec  = OP OM = Hypotenuse side Adjacent side (vi) Cosecant of angle  , written as cosec  = OP MP = Hypotenuse side Opposite side [Note :i) From the above relations, we can say that sin = 1/cosec  or cos  = 1/sec  ii) According to pythagoras theorem, (Hypotenuse side)2 =( Adjacent side)2 + (Opposite side)2