Compare the small angle formula to the large angle formula. In order to analyze the large angle formula, you need to use the Euler Method. The Euler method is a first-order numerical procedure to solve ordinary differential equations. Basically, you take a small step of time and multiply it by the derivate of the value this provides a small change in the value which you then add to the prior value to get the new value. For example, if you know the initial position, you can find the next position by adding the initial position to the initial velocity times the change in time. The velocity can be found a similar way. ( + ) = ( ) + ( ) ∗ ( + ) = ( ) + ( ) ∗