Question

Find the average rate of change of the function over the given interval.. h(t) = cot t, intervals given [pi/4, (3pi)/4]. I've got it all laid out into the proper equation.. h(3pi/4)-h(pi/4)/(3pi/4 - pi/4). with. cot (3pi/4) - cot (pi/4) on the top (numerator). pi/2 on the bottom (denominator).

Answer 1

Hi! All you need to know is that cot stands for cotangent and its the reciprocal of tan i.e. cot(x) = 1/tan(x). You probably know that tan(pi/4) = 1 and that tan(3pi/4) = -1. Happily in these cases it means that cot and tan come out the same (1/1 = 1 and 1/-1 = -1). -1 - (+1) = -2 and this divided by pi/2 = -2/(pi/2) which looks a bit untidy so multiply the top and bottom by 2 (to get rid of the 2 in pi/2) and the answer is -4/pi. HTH