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the period of the function is whatever is multiplying your "x" and something with 2pi...
since nothing is affecting your x...like say: sec(3x).. then it is a normal period
I don't understand it. How you go about doing it?
with this problem, there is nothing to demonstrate... but in general: asin(p(x+sh)) are your important point. a = amplitude sh = horizontal shift p = period and when p is not 1; yor period become: normal period ----------- p
lets take: cos(5x) the normal period for cos is 2pi the period for this setup here would be: 2pi ---- 5
Can you please show me how to do it with this problem? I 'm so confused.
Here is the problem you gave us..make sure its correct and that you havent left anything out... y= -2sec(x+(pi/4))
Yeah, it's right.
ok... can you tell me what the -2 in front of it means?
if you dont know, just give it your best shot
That's the amplitude, right? Other than that I don't know what it means.
that is correct...amplitude is a fancyname for saying: This is how high or low I can go. can you tell me what the "sec" part means?
Sec is 1/x if x=0
good... but a more accurate definition is: 1/cosine all the trig functions have a name, and the name of that function just tells us how to solve for certain parts of a triangle really... now what can you tell me about the inside of the sec function? what does it mean to you?
if sec(x) is when everything is normal.... what have they done to it?
This is where I get confused.
They haven't done anything to it, right?
ill step you thru it :) take your best shot.... when they mess with the normal stuff inside the function, what are they doing?
Changing its degree or shift to a different quadrant. THANKS SO MUCH BTW :)
thats right :) good job
think of the inside of that function as you trying to aim an arrow at the x line.... does this help?
when things are normal inside there, you will hit the "x" everytime... but when things start to get played with and moved around, your aim gets off
You are trying to move across it or go above or below it.
that is correct... now there are 2 ways that they can miss up our aim, by adding stuff or multiplying stuff. each way has a specific affect on our aim...
would the answer be 2pi/-2
nope.... the -2 already played its part, it told us how far to strech the graph up and down.... it doesnt mess with the period or the "phase shift".
when we ADD stuff inside the function it moves us around..left or right.... it shifts us left or right....
would i have to divide 2pi/ (pi/4) which i did but was not right
Not quite... the pi/4 is ADDED to x so it only moves everything left or right.... its called a "shift"
we change the "period" my muliplying or dividing the inside of the function.....
how do we do that though? what do we multiply or divide it by?
can you tell me what a period is in relation to a trig function?
what does the period of a function tell us?
It shows how far the function can move up and down in the y-direction.
not quite, that would be the "vertical" shift... that is not the period. think along the lines of "how long it takes to go thru 1 complete cycle". the graph looks like a wave..usually... and that wave goes up then comes down...then goes under...then comes back to the x axis.... after 1 complete cycle, it has to start over again... does that make sense?
Kind of, isn't a complete cycle 2pi? So every time it hits the x-axis it begins a new cycle?
a complete cycle..or period... for the sin and cos function is 2 pi, that is correct. But remember the graphs of these things if you can. they hit the x line twice, in one cycle. A NEW cycle begins when they are back to their original starting place and have to go thru the motions again. It is like a spinning wheel, every time the wheel makes 1 complete turn, it has gone thru 1 period.
I understand that, but still confused on how to go on with the problem?
Can I substitute 0 in for x and solve from there?
ok.... The period is affected when they "multiply" or "divide" that X buy a number. that number tells the graph to speed up along it period or to slow down and draw out its period... the inside of your function here is: (x + pi/4) Is there a number that is multiplying the "x"?
im here :)
ok.... now as I was on break.... I was thinking aboout what it is you might be asking for with this problem. Are you sure it is the "period" that you want to find? Or is it the values that the period is in, like pi/4 to 8pi/4 like that?
Yeah, on my homework it asks me to find the period of the function.
then ill continue as before..... the period of the function. Now, you said that there was a number that was "multiplying" the inside of our function: (x+ pi/4) what number do you see that is multiplying this?
ill give you a hint, if there is a number multiplying this function it would be standing in fronnt of our "x"
x is multiplying i think
the sec is the name of our function, not a multiplier....
is there a number in front of our x? ( ___ x+ pi/4) ^ is there a number right here in this spot?
lol.....good job :) since there is no number there, our period is normal. the normal period for a sec function is 2pi
what if there had been a number there, how would we have found the period of this function? do you know?
I was about to ask the same thing lol We would have to multiply the number by 2pi, wrong?
divide.... think divide. the period would be equal to: 2pi ------- number
So for example: If the number was 3x, we would divide 2pi/3
that is correct.....
now remember, the tan and cot have a normal period of just "pi".... so that would be the top when you have to deal with those
So if there is no number then the answer is just 2pi?
correct, no number is just 2pi..... or if the function is a tan or cot... its just pi
Does it matter if the degrees are the different? Such as what if it was -2sin?
-2sin(x) has a period of 2pi since there is no number in front of our x value.
just aim into the inside of the function, and forget everything else around it....
Ok, is possible for you to help me with one more?
maybe.... whatcha got?
good, I take it that that is (1/10) tan..... or is that tan supposed to be under the fraction ?
ok.... so whats our question for this one?
Same one, find the period for this function?
recall what the normal period for the tan function is.... do you remember it? is it 2pi or pi ?
yeah, so i would have to divide 2pi/pi in this case
i'm sorry pi
youve got the right idea.... but first we need to know what the normal period for the tan function is....
yes...very good :)
the answer would be 1 then?
yep, it repeats itself after every 1.
instead of repeating at every 3.14; it repeats itself here ate every 1
so for this problem y= -7sec(x) the answer would be 2pi
thats correct :)
got it. you are so much better than my professor. THANK YOU SO MUCH!!!
lol .... maybe :) youre welcome
No, believe you are :)
ive just got more time to devout to teaching it.... but thanx :)
for y= sec(2x+(3pi/2)) would the answer be 2pi/2x= 3.14x