### Abstract:

Fourier transforms are integral ones, We get from Fourier integral treatments. Integral transforms are very important applications. The greater significance of Fourier transforms in general is in their great ability to get solutions of the partial differential equations and the ordinary ones; they also facilitate getting solutions of many integral equations. Fourier transforms depend on Fourier series which have a great importance in approximating functions in form of infinite series from sine and cosine functions at the same time. Or representing each one individually. Fourier infinite transforms in both types: there is What is called Fourier sine and cosine transforms and their reverse transforms. Moreover, that helped to create a great scientific revolution in solving differential equations, particularly, the partial differential equations, besides the questions with initial and marginal conditions. Partial differential equations have many applications in the different sciences, particularly in physics where physical questions appear when they are formulated mathematically in form of partial differential equations accompanied with initial and marginal conditions (physical conditions). Its importance is in giving solutions to these questions that are characterized with clarity and accuracy to fulfill those physical conditions. The study aims to get accurate, easy and quick solutions for the partial differential equations by applying Fourier infinite sine and cosine transforms where the partial differential equation is transformed into ordinary differential equation to be solved as an ordinary differential equation according to its type. The study discussed how to solve Laplace equations and other as an application of the partial differential equations by using Fourier sine and cosine transforms, this gives an easy and accurate solution of physics equations. The descriptive inductive method was adopted. Among the most important results revealed by the study are : how to approximate functions in form of infinite series from the sine and cosine functions. As shown in this study that Fourier infinite sine and cosine transforms are capable of providing distinct solutions for the differential equations in an easy simple way. Thus, the study recommends the necessity of expansion in using Fourier infinite sine and cosine transforms to get accurate solutions particularly in the questions of physical nature.