MAT 1332 : MAT1332 Additional Course Notes 2010
5 Jul 2013
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In particular, the function is de ned for all x that are not odd multiples of , and the function is monotone increasing, see figure 1. The inverse of the tangent is denoted as arctan or tan 1 and it is de ned in the usual way as arctan(tan(x)) = x, tan(arctan(x)) = x. We di erentiate the rst equality above by the chain rule and nd d dx dx x = 1. Hence, we can divide with y = tan(x), since d. [arctan(tan(x))] = d dy arctan(y) d dx tan(x) = 1, d dy arctan(y) = We can now integrate the derivative of the arctan function to get (cid:90) Figure 1: graphs of the tangent function and its inverse, the arctangent function. The e. coli bacterium has a rod-like shape with a cylinder in the middle and two half balls at the ends. The volume of a cylinder with radius r and height h is r2h.
