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pablobeginsBest ResponseYou've already chosen the best response.0
I need 1,2,5, and 1024
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
I'm just not grasping the concept.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
one thing that might help is to rewrite sec, or maybe even tan. into equivalent terms
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
well, tan = sin/cos, right? and sec = 1/cos .... that might help us see the resemblence
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
\[\frac{sin (πx/4)}{cos (πx/4)} < \frac{1}{2}\frac{1}{cos(πx/4)}\] 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
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
since the denominators are the same, lets equate numberators
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
so now we graph the equation to find the point?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
sin (t) < 1/2; well, when does sin(t) = 1/2?
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
how would we go about the analysis?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
divide each side by 2 to get: sin(t) < 1/2 im using "y" to help clean up the argument
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
"t" that is ... cant type ;)
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
that's not one of the choices though :/ ,
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
why would it be? we are only in the middle of it
 2 years ago

GTBest ResponseYou've already chosen the best response.0
Hang in there and understand the steps.
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
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.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
it would be good to remember the basic angles of trig; i believe this is one of them
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323627720794:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
sin(t) = 1/2, when t = 30 degrees, or pi/6
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
is that the special right triangle?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
i have to remember the interval: pi/4 to pi/4, that is between 45 and 45 degrees if i recall it correctly
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
its part of our initial interval; and sin(pi *1/4) is less than 1/2
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
i see. so for number 2 i would just multiply our original interval?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
or would it not change?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
like, number 1 was right, but 2f changed it in some way, because now it's not the same
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
\[2*\frac{sin (πx/4)}{cos (πx/4)} < 2*\frac{1}{2}\frac{1}{cos(πx/4)}\] \[\frac{2sin (πx/4)}{cos (πx/4)} < \frac{1}{cos(πx/4)}\] \[2sin (πx/4) < 1\] \[sin (πx/4) < 1/2\] it looks to be the same
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
must be a problem with the software. now for number 5,i cant tell the graphs apart
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
which one is number 5? this thing is hard to follow
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
graph for y=csc (x)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
well, I know csc is the humpbacks of sinedw:1323628829369:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
the closest one I see is A
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
we can draw the sin(x) in A and see that csc rides the humpbacks
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
yeah, me too! thanks so much
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
id ditch the graph... see that sqrt(3)? that comes about in the 306090 triangle
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
so we would relate the degrees with a sin fuction?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323629102467:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
almost; lets draw the 306090 tri again and see what cot comes from
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323629160526:dw the basic angle is then cot(30) do you agree? 30 = pi/6
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
yeah, i see where you're coming from
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
q2: 18030 = 150 degrees q4: 360  30 = 330 degrees
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
hmmm, 5pi/6 and 11pi/6 seem to fit in there somewhere. but i do get these mixed aroung at times :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
i see the interval now; it one full revolution forward and one full revolution backwards
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
it sent a previous message
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
would the pi/6 be negative? since were dealing with cot?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323629494595:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
pi/6, 5pi/6, 7pi/6, 11pi/6 is my best assessment
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
thats option 4 right?
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
for 11, is the period 16/
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
YES, YOU WERE RIGHT ONCE AGAIN! :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
that doesnt work out right ....
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
if we divide it by 2pi, you get 16
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
that does sound familiar :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
divide by pi; since this is a pi period 2pi is for sin and cos
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
so it would be 1/8?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
pi/(pi/8) = pi * 8/pi = 8
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
and the normal period is 8??
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
tan/cot has a normal pf pi everything else is 2pi
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
since w = pi/8 .... we plug it in
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
we end up with 1/8.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
\[\frac{pi}{pi/8}=\frac{pi*8}{pi}=8\]
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
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.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
since csc rides the humpbacks of sin; lets equate this to an angle of sin. csc = 1/sin is a good thing to remember
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
\[csc(x)=\frac{2\sqrt{3}}{3}\] \[\frac{1}{sin(x)}=\frac{2\sqrt{3}}{3}\] \[\frac{sin(x)}{1}=\frac{3}{2\sqrt{3}}\] and draw a triangle to help visualise it
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323630627950:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
this doesnt seem to match any of our basic triangles does it?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
maybe .... divide off sqrt(3) 2sqrt(3)/sqrt(3) = 2 3/sqrt(3) = 3sqrt(3)/3 = sqrt(3) its our 306090 in disguise
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323630843700:dw
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
so we're just rearranging the equation so the triangle makes sense, in a way
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
\[csc(60) = \frac{2}{\sqrt{3}}\] \[csc(60) = (\frac{2}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}})\] \[csc(60) = \frac{2\sqrt{3}}{3}\] so we are good :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
60 = pi/3 .... so we need to adapt that to the interval
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323631158475:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323631248664:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
thatss what, option 7?
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
seven is incorrect :(nt and so is 3
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
trig takes alot of mental gymnastics :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
i think I know where I went astray at
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
csc is only positive in q1 and q2, i confused it with a tan ....
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1323631597639:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
5,4,1,2 , might be better 3
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
what choice is that?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
option 4, since that aint in the choices
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
youre right tho, these ARE really annoying ;)
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
finally correct! this thing penalizes me for every wrong answer too... now for the period of number 13, is 7?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
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
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
ow do we find the frequency?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
frequency is how fast it moves along .... id have to look it up :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
http://regentsprep.org/Regents/math/algtrig/ATT7/graphvocab.htm
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
i dont recall ever doing an initial phase ...
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
is that a phase shift perhaps?
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
it says initial phase, it might be referring to the same thing
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
i cant make any sense of the online stuff. I doubt that it is the same thing then
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
initial phase is when t=0 ....
 2 years ago

amistre64Best ResponseYou've already chosen the best response.1
but i got no idea at the moment what the means
 2 years ago

pablobeginsBest ResponseYou've already chosen the best response.0
what about the period of 1 7? i got 10/9, but that's apparently wrong
 2 years ago
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