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

I'm just not grasping the concept.

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

how so?

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

since the denominators are the same, lets equate numberators

2sin(pi x/4) < 1

so now we graph the equation to find the point?

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

how would we go about the analysis?

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

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

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

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

Hang in there and understand the steps.

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

|dw:1323627720794:dw|

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

is that the special right triangle?

it is

why the -1?

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

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

or would it not change?

its not it.

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

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

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

graph for y=csc (x)

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

the closest one I see is A

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

yeah, me too! thanks so much

number 10?

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

so we would relate the degrees with a sin fuction?

|dw:1323629102467:dw|

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

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

yeah, i see where you're coming from

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

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

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

ignore that

it sent a previous message

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

|dw:1323629494595:dw|

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

thats option 4 right?

for 11, is the period 16/

YES, YOU WERE RIGHT ONCE AGAIN! :)

that doesnt work out right ....

if we divide it by 2pi, you get 16

that does sound familiar :)

but the 2pi is wrong

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

so it would be 1/8?

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

normal period/w

and the normal period is 8??

look again

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

pi/(w) = periodicity

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

we end up with 1/8.

\[\frac{pi}{pi/8}=\frac{pi*8}{pi}=8\]

|dw:1323630627950:dw|

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

|dw:1323630843700:dw|

'disguise' lol

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

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

|dw:1323631158475:dw|

|dw:1323631248664:dw|

thatss what, option 7?

seven is incorrect :-(nt and so is 3

trig takes alot of mental gymnastics :)

hmmm

i think I know where I went astray at

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

|dw:1323631597639:dw|

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

what choice is that?

option 4, since that aint in the choices

youre right tho, these ARE really annoying ;)

ow do we find the frequency?

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

http://regentsprep.org/Regents/math/algtrig/ATT7/graphvocab.htm

freq = 1/period

initial phase?

i dont recall ever doing an initial phase ...

is that a phase shift perhaps?

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

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

initial phase is when t=0 ....

but i got no idea at the moment what the means

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