1. To calculate a planet's space coordinates, we have to solve the function f(x)x10.5sinx. Let the base point be ax12 on the interval [0,]. (a) Determine the lowest order Taylor series expansion which results in a minimum error of 0.015 with the maximum step size possible on the specified interval. (step 2 (b) Using the Taylor series identified in a, decrease the step size by factors of 2, 5, 10 and 20 , and create a plot of the calculated error at location as a function of step size. (c) For the step size increments above, determine the number of terms in the Taylor series needed to meet the minimum error 0.015. Create a plot of the number of terms versus the step size