## anonymous 5 years ago h(t)=cot t , itervals given, π/4,3π/4 finally got the equation written out, took me and while to figure it out, sorry. book answer is -4/pi but I have no idea how to set this up

1. amistre64

set up for?

2. anonymous

what does it mean "the answer is $-\frac{4}{\pi}$? there is no question, just a definition of a function $h(t)=\cot(t)$

3. anonymous

average rate of change

4. anonymous

oh that is a question!

5. anonymous

sorry, duh

6. amistre64

average rate of change:$\frac{change. in. y}{change.in.x}$from begining to end

7. anonymous

$\frac{h(\frac{3\pi}{4})-h(\frac{\pi}{4})}{\frac{3\pi}{4}-\frac{\pi}{4}}$

8. amistre64

$\frac{cot(3pi/4)-cot(pi/4)}{3pi/4-pi/4}$

9. amistre64

latex is slowing me down lol

10. anonymous

i can do the bottom: $\frac{3\pi}{4}-\frac{\pi}{4}=\frac{\pi}{2}$

11. amistre64

can we factor out a cot up top?

12. anonymous

lol, right

13. amistre64

tanpi/4 = 1; flip for cot = 1 tan3pi/4 = -1; flip for cot = -1

14. amistre64

-1-1 = -2 for the top

15. amistre64

$\frac{-2}{pi/2}=-\frac{4}{pi}$

16. anonymous

I swear math makes me seriously think I may be retarded, I just cant understand it. Very difficult for my 30 year old brain. LOL...

17. amistre64

just wait till your my age :)

18. anonymous

I hope I catch on fairly quickly because I have to pass this course.

19. anonymous

Thank you both very much!!

20. anonymous

30!! i never met anyone so old....

21. anonymous

I know! Old as dirt! LOL, at least that is how Cal. makes me feel anyway, I should know this stuff :(

22. anonymous

Sorry to jump in after 7months on this question, but I'm having trouble understanding how you factored out the cot for the top. I'm getting stuck at $\cot(3\pi/4)−\cot(\pi/4)$ How did you arrive at 1 and -1 for the top? I plugged it into my calculator and it came up something like 0.01something.

23. amistre64

i believe that 7 months ago that was a joke :) pi/4 radians is equivalent to 45 degrees. the tangent of an angle is the slope of the line that the radius makes with the positive x axis. the cotangent is just the inverse of the tangent. |dw:1346155666663:dw| tan(pi/4) = n/n = 1, the inverse of 1 is: 1 when we have three pi/4 s, we end up with a 135 degree angle; |dw:1346155817540:dw| as such; tan(3pi/4) = -n/n = -1, the inverse is: -1 -1 - (1) = -2

24. anonymous

Ah! Thank you so much! I got the beginning bit, and the last bit, but not the actual cot bit. My prof skipped the pre-cal review, and in retrospect I knew I should've looked it over before classes started. Thanks for going into such depth, really helps. ^_^