The function \textcsc(\theta) , or cosecant, is a trigonometric function defined as the reciprocal of the sine function. In mathematical terms, \textcsc(\theta) = \frac1\sin(\theta) . It is used to relate the angles of a triangle to the ratios of its sides, particularly in right triangles. The cosecant function is defined for all angles \theta where \sin(\theta) is not equal to zero. This means \textcsc(\theta) is undefined at angles like 0^\circ and 180^\circ . Cosecant is often used in various applications, including physics and engineering, where wave functions and oscillations are analyzed.