In this paper we illustrate some novel procedures of using Sine methods to compute solutions to three types of medical problems. The first of these is a novel way to solve optimal control problems, the second is an original way to reconstruct images for X-ray tomography, and the third is a novel way to do ultrasonic tomography inversion. Each of these procedures uses Sine convolution, which is a novel computational procedure for obtaining accurate approximations to-indefinite convolutions.