A transcendental function is a type of mathematical function that cannot be expressed as a finite sequence of algebraic operations (addition, subtraction, multiplication, division, and taking roots). Common examples include the exponential function, logarithmic function, and trigonometric functions like sine and cosine. These functions often arise in various fields of science and engineering. Transcendental functions are essential in calculus and analysis, as they help describe complex phenomena. For instance, the function e^x (the exponential function) is widely used in growth models, while sin(x) and cos(x) are crucial in wave mechanics and oscillatory motion.