How do I find the period of this function?
y= -2sec(x+(pi/4))

- anonymous

How do I find the period of this function?
y= -2sec(x+(pi/4))

- chestercat

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- amistre64

the period of the function is whatever is multiplying your "x" and something with 2pi...

- amistre64

since nothing is affecting your x...like say: sec(3x).. then it is a normal period

- anonymous

I don't understand it. How you go about doing it?

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## More answers

- amistre64

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

- amistre64

lets take:
cos(5x)
the normal period for cos is 2pi
the period for this setup here would be:
2pi
----
5

- anonymous

Can you please show me how to do it with this problem? I 'm so confused.

- amistre64

Here is the problem you gave us..make sure its correct and that you havent left anything out...
y= -2sec(x+(pi/4))

- anonymous

Yeah, it's right.

- amistre64

ok...
can you tell me what the -2 in front of it means?

- amistre64

if you dont know, just give it your best shot

- anonymous

That's the amplitude, right? Other than that I don't know what it means.

- amistre64

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?

- anonymous

Sec is 1/x if x=0

- amistre64

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?

- amistre64

if sec(x) is when everything is normal.... what have they done to it?

- anonymous

This is where I get confused.

- anonymous

They haven't done anything to it, right?

- amistre64

ill step you thru it :)
take your best shot.... when they mess with the normal stuff inside the function, what are they doing?

- anonymous

Changing its degree or shift to a different quadrant. THANKS SO MUCH BTW :)

- amistre64

thats right :) good job

- amistre64

think of the inside of that function as you trying to aim an arrow at the x line.... does this help?

- amistre64

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

- anonymous

You are trying to move across it or go above or below it.

- amistre64

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...

- anonymous

would the answer be 2pi/-2

- amistre64

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".

- amistre64

when we ADD stuff inside the function it moves us around..left or right.... it shifts us left or right....

- anonymous

would i have to divide 2pi/ (pi/4) which i did but was not right

- amistre64

Not quite... the pi/4 is ADDED to x so it only moves everything left or right.... its called a "shift"

- anonymous

so pi/4x?

- amistre64

we change the "period" my muliplying or dividing the inside of the function.....

- anonymous

how do we do that though? what do we multiply or divide it by?

- amistre64

can you tell me what a period is in relation to a trig function?

- amistre64

what does the period of a function tell us?

- anonymous

It shows how far the function can move up and down in the y-direction.

- amistre64

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?

- anonymous

Kind of, isn't a complete cycle 2pi? So every time it hits the x-axis it begins a new cycle?

- amistre64

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.

- anonymous

I understand that, but still confused on how to go on with the problem?

- anonymous

Can I substitute 0 in for x and solve from there?

- amistre64

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"?

- anonymous

yes

- amistre64

im here :)

- anonymous

i'm ready

- amistre64

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?

- anonymous

Yeah, on my homework it asks me to find the period of the function.

- amistre64

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?

- amistre64

ill give you a hint, if there is a number multiplying this function it would be standing in fronnt of our "x"

- anonymous

x is multiplying i think

- anonymous

the sec?

- amistre64

the sec is the name of our function, not a multiplier....

- amistre64

is there a number in front of our x?
( ___ x+ pi/4)
^
is there a number right here in this spot?

- anonymous

no

- amistre64

lol.....good job :) since there is no number there, our period is normal. the normal period for a sec function is 2pi

- amistre64

what if there had been a number there, how would we have found the period of this function? do you know?

- anonymous

I was about to ask the same thing lol We would have to multiply the number by 2pi, wrong?

- amistre64

divide.... think divide.
the period would be equal to:
2pi
-------
number

- anonymous

So for example: If the number was 3x, we would divide 2pi/3

- amistre64

that is correct.....

- amistre64

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

- anonymous

So if there is no number then the answer is just 2pi?

- amistre64

correct, no number is just 2pi..... or if the function is a tan or cot... its just pi

- anonymous

Does it matter if the degrees are the different? Such as what if it was -2sin?

- amistre64

-2sin(x) has a period of 2pi since there is no number in front of our x value.

- amistre64

just aim into the inside of the function, and forget everything else around it....

- anonymous

Ok, is possible for you to help me with one more?

- amistre64

maybe.... whatcha got?

- anonymous

y= 1/10tan(pi(x)-pi)

- amistre64

good, I take it that that is (1/10) tan..... or is that tan supposed to be under the fraction ?

- anonymous

(1/10)tan

- amistre64

ok.... so whats our question for this one?

- anonymous

Same one, find the period for this function?

- amistre64

recall what the normal period for the tan function is.... do you remember it? is it 2pi or pi ?

- anonymous

yeah, so i would have to divide 2pi/pi in this case

- anonymous

i'm sorry pi

- amistre64

youve got the right idea.... but first we need to know what the normal period for the tan function is....

- anonymous

pi/pi then?

- amistre64

yes...very good :)

- anonymous

the answer would be 1 then?

- amistre64

yep, it repeats itself after every 1.

- amistre64

instead of repeating at every 3.14; it repeats itself here ate every 1

- anonymous

so for this problem y= -7sec(x) the answer would be 2pi

- amistre64

thats correct :)

- anonymous

got it. you are so much better than my professor. THANK YOU SO MUCH!!!

- amistre64

lol .... maybe :) youre welcome

- anonymous

No, believe you are :)

- anonymous

me*

- amistre64

ive just got more time to devout to teaching it.... but thanx :)

- anonymous

for y= sec(2x+(3pi/2)) would the answer be 2pi/2x= 3.14x

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