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).

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Mathematics

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8 February, 09:12

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).

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Andy Cooke · 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