35. Inverse Tangent Series and an Approximation for Tr: You recall that tan(7 /4) = 1. Thus tan '1 = Tr/4. In this problem you will use the inverse tangent series to estimate TT. a. Write the first few terms of the Maclaurin series for tan '1. Then use the appropriate features of your grapher to find the 10th partial sum of this series. Multiply by 4 to find an approximate value of 7. How close does this approximation come to TT? b. Find another approximation for or using the 50th partial sum of the series in 35a. Is this approximation much better than the one using the 10th partial sum? c. By appropriate trigonometry, show that tan '1 = tan , + tan Use the result to write 7 /4 as a sum of the Maclaurin series. Estimate the value of ir by finding the tenth partial sums of the two series. Comment on how much better this method is for estimating or than the methods of 35a and 35b