The Distance Formula For Polar Coordinates

 

     Suppose we are given two points in polar coordinates,  and . We want to show that the distance between the two points is .

 

    

 

 

     Recall that the distance formula for rectangular coordinates is given by the equation .

 

     Using the fact that  and , we can derive the desired distance formula.

 

     

 

     And so, we have shown the desired formula. Notice that the order of  and  does not matter, since  because cosine is an even function.