Tangential acceleration is the rate of change of an object's tangential velocity. It is the component of acceleration that is parallel to the direction of motion.
Radial acceleration is the rate of change of an object's radial velocity. It is the component of acceleration that is perpendicular to the direction of motion and points towards the center of the circular path.
Tangential acceleration can be calculated by dividing the change in tangential velocity by the change in time. It can also be calculated by multiplying the tangential velocity by the angular acceleration, where the angular acceleration is the rate of change of the object's angular velocity.
Radial acceleration can be calculated by dividing the change in radial velocity by the change in time. It can also be calculated by squaring the object's tangential velocity and dividing it by the radius of the circular path.
Sin and cos are used to calculate the components of tangential and radial acceleration, respectively. The sine of the angle between the object's tangential velocity and the reference frame represents the magnitude of the tangential acceleration, while the cosine of the angle between the object's radial velocity and the reference frame represents the magnitude of the radial acceleration.