## lsugano 2 years ago i want to graph 3csc2x but I dont know how!! can someone help me with steps!??

1. AravindG

do u knw the graph of cosec x?

2. Kainui

One way might be to try rewriting 3csc(2x) as 3/sin(2x). Then from here, mark on your graph where one period should end and where the amplitude should be. Since it's 1/sin it will be "upside down" Look at this picture to give yourself some help along the way so that next time you can see. http://www.wolframalpha.com/input/?i=%203csc(2x)&t=crmtb01 The main points to hit when graphing any trig function are what it looks like at 0, T/4, T/2, 3T/2, and T, since it repeats after that and you can kind of "guess" by filling in the points between where the curve should look like.

3. lsugano

i know that cscx = 1/sinx

4. lsugano

so if i put that function... 3/sin(2x)?

5. AravindG

i can help with an alternate solution ..but for that you need to answer my queries

6. lsugano

the graph of csc ..yes i do know what it is!

7. Kainui

Find the amplitude and period.

8. AravindG

well thats great...now what you need to understand is that the graph of cosec 2x will be same as cosec x only difference is that we have to minimize the graph to t=pi

9. AravindG

let me show u how i do that for sin 2x

10. AravindG

|dw:1355991064248:dw|

11. AravindG

did you get that ?

12. lsugano

sin2x makes the half of sinx

13. AravindG

yep similiar is what happens for cosec 2x

14. AravindG

its like bending a spring to half its normal position from one side

15. lsugano

okay!

16. AravindG

now ...we are 80% over !

17. lsugano

ok!!

18. AravindG

well next step is to increase the magnitude of cosec 2x 3 times

19. lsugano

does that mean the maximum is at 3??

20. AravindG

think again :)

21. lsugano

i mean min 3, max3

22. AravindG

yepp !!

23. lsugano

okay...so what do i do next?

24. AravindG

we actually dont need pencil or paper just our mind to visualize this !!

25. AravindG

we are done !! this is ur graph !!

26. lsugano

oh yeah!!! omgsh thank you so much!!! wait im gonna do a quick sketch

27. AravindG

well see hw elegantmethod it is when compared to normal working that we do mechanically (see kainnui's re[ly)

28. lsugano

|dw:1355991527707:dw|

29. AravindG

mark angles pls

30. lsugano

|dw:1355991626300:dw|

31. lsugano

is it correct?

32. AravindG

exactlyy !! well done !!

33. lsugano

Ah thank you so much!!! you're an amzing teacher!!

34. AravindG

you did it yourself !! cngrts!!

35. AravindG

remember:always use ur visualization power as the first resort to solve math problems..it really simplifies ur work !! good luck!

36. Kainui

Yeah, awesome, you're a quick learner Isugano.