Question

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

Answer 1

set up for?

Answer 2

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

Answer 3

average rate of change

Answer 4

oh that is a question!

Answer 5

sorry, duh

Answer 6

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

Answer 7

\[\frac{h(\frac{3\pi}{4})-h(\frac{\pi}{4})}{\frac{3\pi}{4}-\frac{\pi}{4}}\]

Answer 8

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

Answer 9

latex is slowing me down lol

Answer 10

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

Answer 11

can we factor out a cot up top?

Answer 12

lol, right

Answer 13

tanpi/4 = 1; flip for cot = 1

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

Answer 14

-1-1 = -2 for the top

Answer 15

\[\frac{-2}{pi/2}=-\frac{4}{pi}\]

Answer 16

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...

Answer 17

just wait till your my age :)

Answer 18

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

Answer 19

Thank you both very much!!

Answer 20

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

Answer 21

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

Answer 22

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.

Answer 23

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.


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;


as such; tan(3pi/4) = -n/n = -1, the inverse is: -1

-1 - (1) = -2