## ta123 4 years ago need help on the attachment

1. ta123

2. LagrangeSon678

come on no has helped you with this yet?

3. ta123

no

4. LagrangeSon678

should i solve this or go to sleep.....

5. ta123

6. ta123

Oops! forgot to sleep after going

7. LagrangeSon678

okay, first things first, lets find the first derivaitve of the function your where given

8. LagrangeSon678

can you find it?

9. ta123

9sec^(2)x

10. LagrangeSon678

okay good

11. LagrangeSon678

now can you please evaluate: f(pi/4)=9sec^2(pi/4)

12. ta123

square root of 2

13. ta123

is it right?

14. LagrangeSon678

basically to make it more accesible we can write this as: f(pi/4)=9[sec(pi/4)]^2

15. LagrangeSon678

further more we can write it as: f(pi/4)=9[1/cos(pi/4)]^2

16. LagrangeSon678

then evalutaing we get: f(pi/4)=9[1/sqrt(2)/(2)]^2

17. ta123

what square root 2/2???

18. LagrangeSon678

further: f(pi/4)=9[sqrt(2)]^2 which the gives us: f(pi/4)=9(2), which is 18 Thus f(pi/4)=18

19. LagrangeSon678

yes, look at the unit circle, at pi/4 or 45 degrees, cos is sqr(2)/2, now if we rationalize the numerator we get just sqrt(2)

20. ta123

21. LagrangeSon678

i rewrote secx as 1/cosx

22. ta123

how come?

23. LagrangeSon678

just to make is easier for me, but if realise that sec(pi/4) is sqrt(2) then more power to you

24. LagrangeSon678

Now we have found the slope (m) of our line, it is 18

25. ta123

y-y=m(x-x)

26. LagrangeSon678

yes, but we will use this form, y=mx+b

27. LagrangeSon678

i am getting sleepy lets finish this problem

28. ta123

ok

29. ta123

what would be the b in the slope formula

30. LagrangeSon678

Now remeber we said, that we have the x coordinate in the beining of pi/4, lets evaluate the orginal function at this point, this will give us the y in our line. f(pi/4)=9tan(pi/4) =9(1) =9 now we have our x which is pi/4, we have our slope which is 18, lets plug this info into our line: 9=18(pi/4)+b this means that b is = to 9-18pi/4

31. LagrangeSon678

now lets substitute everyting in: y=18x-(36-18pi)/(4)

32. LagrangeSon678

are we good?

33. ta123

36??

34. LagrangeSon678

i combined 9 and 18pi/4

35. LagrangeSon678

yes?

36. ta123

still don't see how you can 36??

37. LagrangeSon678

|dw:1316152625201:dw|

38. ta123

you could've just simplify it to 9pi/2

39. LagrangeSon678

okay, then smarty pants do it your way, regardless we came to a correct answer

40. ta123

sorry, so the finally would look like this 18x+9(1-pi/2)

41. LagrangeSon678

sure

42. ta123

I just look the answer choices and so which one was the closest, but how come they have it 18x+9(1-pi/2) instead of just 18x+9pi/2

43. LagrangeSon678

distribute the negative sign, first

44. ta123

huh?

45. ta123

what negative sign?

46. LagrangeSon678

|dw:1316153351852:dw|

47. LagrangeSon678

got it ?

48. ta123

but was there a 9-18pi/4 at the beginning

49. LagrangeSon678

yes there was

50. LagrangeSon678

can you not see it: |dw:1316153548845:dw|

51. ta123

I meant why was 9-18pi/4 at the begginig

52. LagrangeSon678

above i accidentally wrote:y=18x-(36-18pi)/(4), but is was really suppose to be : y=18x+(36-18pi)/(4), sorry about the typo

53. LagrangeSon678

okay, so can we lay this problem to rest?

54. ta123

I guess, but still don't get why they have 9-18pi/4 plug into b instead of just 18pi/4 by itself

55. LagrangeSon678

Now remeber we said, that we have the x coordinate in the beining of pi/4, lets evaluate the orginal function at this point, this will give us the y in our line. f(pi/4)=9tan(pi/4) =9(1) =9 now we have our x which is pi/4, we have our slope which is 18, lets plug this info into our line: 9=18(pi/4)+b this means that b is = to 9-18pi/4

56. LagrangeSon678

|dw:1316153804630:dw|

57. ta123

oh, ok now we can lay this problem to rest, thanks so much for being patience

58. LagrangeSon678

its good you ask questions, i know i can confusing sometimes :)

59. ta123

Thanks for giving me a metal

60. ta123

yeah I just want to understand the problem instead of just getting the answer

61. ta123

because I might see it on the test, but thanks again

62. LagrangeSon678

anytime