# Trignometry - Basics- Quantitative Aptitude

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In a right angled triangle as shown in the figure below, the 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), is defined as the ratio of the side opposite the angle to the hypotenuse.
${\displaystyle \sin A={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}={\frac {a}{\,c\,}}\,.}$
• Cosine function (cos), is defined as the ratio of the adjacent leg to the hypotenuse.
${\displaystyle \cos A={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}={\frac {b}{\,c\,}}\,.}$
• Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
${\displaystyle \tan A={\frac {\textrm {opposite}}{\textrm {adjacent}}}={\frac {a}{\,b\,}}={\frac {a}{\,c\,}}*{\frac {c}{\,b\,}}={\frac {a}{\,c\,}}/{\frac {b}{\,c\,}}={\frac {\sin A}{\cos A}}\,.}$

The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively:
${\displaystyle \csc A={\frac {1}{\sin A}}={\frac {\textrm {hypotenuse}}{\textrm {opposite}}}={\frac {c}{a}},}$
${\displaystyle \sec A={\frac {1}{\cos A}}={\frac {\textrm {hypotenuse}}{\textrm {adjacent}}}={\frac {c}{b}},}$
${\displaystyle \cot A={\frac {1}{\tan A}}={\frac {\textrm {adjacent}}{\textrm {opposite}}}={\frac {\cos A}{\sin A}}={\frac {b}{a}}.}$