Find the exact length of the curve. use a graph to determine the parameter interval.

r = cos^2(theta/2)

The formula for the length of a polar curve is∫r2+(dr/dθ)2 from a to b. 

In this case, dr/dθ is the derivative of the function r which is equal to -cos (theta/2) * sin (theta/2) which is equal to -1/2 cos theta. Since there are no limits defined, we leave the formula as it is but one can use the calculator if there are limits present already

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.

The slope best fit isc. 1/6 mile per hour