## pablobegins Group Title Really annoying trigonometric graphing, help! 2 years ago 2 years ago

1. pablobegins Group Title

2. pablobegins Group Title

I need 1,2,5, and 10-24

3. pablobegins Group Title

I'm just not grasping the concept.

4. amistre64 Group Title

f(x) = tan πx/4 g(x) =1/2 sec πx/4 Approximate the interval where f < g. lets set this up then, we know f and g tan (πx/4) < 1/2 sec(πx/4)

5. amistre64 Group Title

one thing that might help is to rewrite sec, or maybe even tan. into equivalent terms

6. pablobegins Group Title

how so?

7. amistre64 Group Title

well, tan = sin/cos, right? and sec = 1/cos .... that might help us see the resemblence

8. amistre64 Group Title

$\frac{sin (πx/4)}{cos (πx/4)} < \frac{1}{2}\frac{1}{cos(πx/4)}$ we can get rid of that 1/2 by multiplying by 2 $\frac{(2)sin (πx/4)}{cos (πx/4)} < \frac{1(2)}{2}\frac{1}{cos(πx/4)}$ $\frac{2sin (πx/4)}{cos (πx/4)} < \frac{1}{cos(πx/4)}$ now it looks better

9. amistre64 Group Title

since the denominators are the same, lets equate numberators

10. amistre64 Group Title

2sin(pi x/4) < 1

11. pablobegins Group Title

so now we graph the equation to find the point?

12. amistre64 Group Title

id stick to the analysis rather than a graph; the graph can be used to dbl chk the results; but i doubt it will give a definitive result

13. amistre64 Group Title

sin (t) < 1/2; well, when does sin(t) = 1/2?

14. pablobegins Group Title

how would we go about the analysis?

15. amistre64 Group Title

divide each side by 2 to get: sin(t) < 1/2 im using "y" to help clean up the argument

16. amistre64 Group Title

"t" that is ... cant type ;)

17. pablobegins Group Title

that's not one of the choices though :/ ,

18. amistre64 Group Title

why would it be? we are only in the middle of it

19. GT Group Title

Hang in there and understand the steps.

20. pablobegins Group Title

OH! Gotcha. I just have a terrible teacher who goes about everything explaining really fast, and then expecting us to know all this. I'm sorry.

21. amistre64 Group Title

it would be good to remember the basic angles of trig; i believe this is one of them

22. amistre64 Group Title

|dw:1323627720794:dw|

23. amistre64 Group Title

sin(t) = 1/2, when t = 30 degrees, or pi/6

24. pablobegins Group Title

is that the special right triangle?

25. amistre64 Group Title

it is

26. amistre64 Group Title

i have to remember the interval: -pi/4 to pi/4, that is between 45 and -45 degrees if i recall it correctly

27. amistre64 Group Title

now i would see about equating pi x/4 and t pi x/4 = pi/6 divide off the pis x/4 = 1/6 and multiply off the 1/4 x = 4/6 , and simplify x = 2/3 so, if i did it right, it should be (-1, 2/3) but if you have questions as to why, it would be good to ask. The numbers tend to be unimportant and it is the process that matters.

28. pablobegins Group Title

why the -1?

29. amistre64 Group Title

its part of our initial interval; and sin(pi *-1/4) is less than 1/2

30. pablobegins Group Title

i see. so for number 2 i would just multiply our original interval?

31. amistre64 Group Title

it would be nice if we could, but no. trig functions are periodic, they do not act like linear functions. so its best to retrace the steps to make sure

32. pablobegins Group Title

or would it not change?

33. amistre64 Group Title

2f just changes how high or low the graph would go; so id guess that its the same intervals. But i would still have to dbl chk the results

34. pablobegins Group Title

its not it.

35. pablobegins Group Title

like, number 1 was right, but 2f changed it in some way, because now it's not the same

36. amistre64 Group Title

$2*\frac{sin (πx/4)}{cos (πx/4)} < 2*\frac{1}{2}\frac{1}{cos(πx/4)}$ $\frac{2sin (πx/4)}{cos (πx/4)} < \frac{1}{cos(πx/4)}$ $2sin (πx/4) < 1$ $sin (πx/4) < 1/2$ it looks to be the same

37. pablobegins Group Title

must be a problem with the software. now for number 5,i cant tell the graphs apart

38. amistre64 Group Title

which one is number 5? this thing is hard to follow

39. pablobegins Group Title

graph for y=csc (x)

40. amistre64 Group Title

well, I know csc is the humpbacks of sine|dw:1323628829369:dw|

41. amistre64 Group Title

the closest one I see is A

42. amistre64 Group Title

we can draw the sin(x) in A and see that csc rides the humpbacks

43. pablobegins Group Title

yeah, me too! thanks so much

44. pablobegins Group Title

number 10?

45. amistre64 Group Title

id ditch the graph... see that sqrt(3)? that comes about in the 30-60-90 triangle

46. amistre64 Group Title

and since cot = cos/sin; this is negative when either cos is negative OR sin is negative; but not both. that occurs in q2 and q4

47. pablobegins Group Title

so we would relate the degrees with a sin fuction?

48. amistre64 Group Title

|dw:1323629102467:dw|

49. amistre64 Group Title

almost; lets draw the 30-60-90 tri again and see what cot comes from

50. amistre64 Group Title

|dw:1323629160526:dw| the basic angle is then cot(30) do you agree? 30 = pi/6

51. pablobegins Group Title

yeah, i see where you're coming from

52. amistre64 Group Title

q2: 180-30 = 150 degrees q4: 360 - 30 = 330 degrees

53. amistre64 Group Title

hmmm, 5pi/6 and 11pi/6 seem to fit in there somewhere. but i do get these mixed aroung at times :)

54. amistre64 Group Title

i see the interval now; it one full revolution forward and one full revolution backwards

55. pablobegins Group Title

ignore that

56. pablobegins Group Title

it sent a previous message

57. pablobegins Group Title

would the pi/6 be negative? since were dealing with cot?

58. amistre64 Group Title

|dw:1323629494595:dw|

59. amistre64 Group Title

-pi/6, 5pi/6, -7pi/6, 11pi/6 is my best assessment

60. amistre64 Group Title

thats option 4 right?

61. pablobegins Group Title

for 11, is the period 16/

62. pablobegins Group Title

YES, YOU WERE RIGHT ONCE AGAIN! :)

63. amistre64 Group Title

tan and cot have a normal period of pi; this speeds that period up; by a factor of 8.; so id say its a period of 1/8

64. amistre64 Group Title

that doesnt work out right ....

65. pablobegins Group Title

if we divide it by 2pi, you get 16

66. amistre64 Group Title

that does sound familiar :)

67. amistre64 Group Title

but the 2pi is wrong

68. amistre64 Group Title

divide by pi; since this is a pi period 2pi is for sin and cos

69. pablobegins Group Title

so it would be 1/8?

70. amistre64 Group Title

pi/(pi/8) = pi * 8/pi = 8

71. amistre64 Group Title

normal period/w

72. pablobegins Group Title

and the normal period is 8??

73. amistre64 Group Title

look again

74. amistre64 Group Title

tan/cot has a normal pf pi everything else is 2pi

75. amistre64 Group Title

pi/(w) = periodicity

76. amistre64 Group Title

since w = pi/8 .... we plug it in

77. pablobegins Group Title

we end up with 1/8.

78. amistre64 Group Title

$\frac{pi}{pi/8}=\frac{pi*8}{pi}=8$

79. pablobegins Group Title

oh, i was solving it incorrectly. can you explain 12 to me please? i know it's similar to 10, but i want to grasp the concept.

80. amistre64 Group Title

since csc rides the humpbacks of sin; lets equate this to an angle of sin. csc = 1/sin is a good thing to remember

81. amistre64 Group Title

$csc(x)=\frac{2\sqrt{3}}{3}$ $\frac{1}{sin(x)}=\frac{2\sqrt{3}}{3}$ $\frac{sin(x)}{1}=\frac{3}{2\sqrt{3}}$ and draw a triangle to help visualise it

82. amistre64 Group Title

|dw:1323630627950:dw|

83. amistre64 Group Title

this doesnt seem to match any of our basic triangles does it?

84. amistre64 Group Title

maybe .... divide off sqrt(3) 2sqrt(3)/sqrt(3) = 2 3/sqrt(3) = 3sqrt(3)/3 = sqrt(3) its our 30-60-90 in disguise

85. amistre64 Group Title

|dw:1323630843700:dw|

86. pablobegins Group Title

'disguise' lol

87. pablobegins Group Title

so we're just rearranging the equation so the triangle makes sense, in a way

88. amistre64 Group Title

$csc(60) = \frac{2}{\sqrt{3}}$ $csc(60) = (\frac{2}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}})$ $csc(60) = \frac{2\sqrt{3}}{3}$ so we are good :)

89. amistre64 Group Title

60 = pi/3 .... so we need to adapt that to the interval

90. amistre64 Group Title

|dw:1323631158475:dw|

91. amistre64 Group Title

|dw:1323631248664:dw|

92. amistre64 Group Title

thatss what, option 7?

93. pablobegins Group Title

seven is incorrect :-(nt and so is 3

94. amistre64 Group Title

trig takes alot of mental gymnastics :)

95. amistre64 Group Title

hmmm

96. amistre64 Group Title

i think I know where I went astray at

97. amistre64 Group Title

csc is only positive in q1 and q2, i confused it with a tan ....

98. amistre64 Group Title

|dw:1323631597639:dw|

99. amistre64 Group Title

-5,-4,1,2 ---------, might be better 3

100. pablobegins Group Title

what choice is that?

101. amistre64 Group Title

option 4, since that aint in the choices

102. amistre64 Group Title

youre right tho, these ARE really annoying ;)

103. pablobegins Group Title

finally correct! this thing penalizes me for every wrong answer too... now for the period of number 13, is 7?

104. amistre64 Group Title

the value attached to x is out "w" and sec is a 2pi normal $\frac{2pi}{-7pi/2}$ $\frac{2pi*2}{-7pi}$ $\frac{2*2}{-7}=-4/7$ id go with option 1

105. pablobegins Group Title

ow do we find the frequency?

106. amistre64 Group Title

frequency is how fast it moves along .... id have to look it up :)

107. amistre64 Group Title
108. amistre64 Group Title

freq = 1/period

109. pablobegins Group Title

initial phase?

110. amistre64 Group Title

i dont recall ever doing an initial phase ...

111. amistre64 Group Title

is that a phase shift perhaps?

112. pablobegins Group Title

it says initial phase, it might be referring to the same thing

113. amistre64 Group Title

i cant make any sense of the online stuff. I doubt that it is the same thing then

114. amistre64 Group Title

initial phase is when t=0 ....

115. amistre64 Group Title

but i got no idea at the moment what the means

116. pablobegins Group Title

what about the period of 1 7? i got 10/9, but that's apparently wrong