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)
I'm stuck with the cot. The book says the solution is 4/pi, and if I skip over the cot part I can sort of see how that works out, but it's the cot that's stalling me.

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

Answer 2

http://openstudy.com/study#/updates/4f1c393ce4b04992dd236cb3

Answer 3

Ah, I didn't know that JohnMartin! Prof skipped straight past the pre-cal review chapter - should've anticipated it, in retrospect. Too many years since I've dabbled in Calculus. Thanks for clarifying.
And thank you amistre64 for the very in depth explanation! Really helped seal it in my head. A big help, thank you.

Answer 4

youre welcome, and good luck