Question

How do I find the period of this function?

y= -2sec(x+(pi/4))

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

lets take:

cos(5x)

the normal period for cos is 2pi

the period for this setup here would be:

2pi
----
5

Answer 6

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

Answer 7

Here is the problem you gave us..make sure its correct and that you havent left anything out...

y= -2sec(x+(pi/4))

Answer 8

Yeah, it's right.

Answer 9

ok...

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

Answer 10

if you dont know, just give it your best shot

Answer 11

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

Answer 12

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?

Answer 13

Sec is 1/x if x=0

Answer 14

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?

Answer 15

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

Answer 16

This is where I get confused.

Answer 17

They haven't done anything to it, right?

Answer 18

ill step you thru it :)

take your best shot.... when they mess with the normal stuff inside the function, what are they doing?

Answer 19

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

Answer 20

thats right :) good job

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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...

Answer 25

would the answer be 2pi/-2

Answer 26

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".

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

so pi/4x?

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

what does the period of a function tell us?

Answer 35

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

Answer 36

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?

Answer 37

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

Answer 38

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.

Answer 39

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

Answer 40

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

Answer 41

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"?

Answer 42

yes

Answer 43

im here :)

Answer 44

i'm ready

Answer 45

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?

Answer 46

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

Answer 47

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?

Answer 48

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

Answer 49

x is multiplying i think

Answer 50

the sec?

Answer 51

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

Answer 52

is there a number in front of our x?

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

Answer 53

no

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

divide.... think divide.

the period would be equal to:

2pi
-------
number

Answer 58

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

Answer 59

that is correct.....

Answer 60

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

Answer 61

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

Answer 62

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

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

maybe.... whatcha got?

Answer 68

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

Answer 69

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

Answer 70

(1/10)tan

Answer 71

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

Answer 72

Same one, find the period for this function?

Answer 73

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

Answer 74

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

Answer 75

i'm sorry pi

Answer 76

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

Answer 77

pi/pi then?

Answer 78

yes...very good :)

Answer 79

the answer would be 1 then?

Answer 80

yep, it repeats itself after every 1.

Answer 81

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

Answer 82

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

Answer 83

thats correct :)

Answer 84

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

Answer 85

lol .... maybe :) youre welcome

Answer 86

No, believe you are :)

Answer 87

me*

Answer 88

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

Answer 89

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