Question

4. Sketch the grap

Answer 1

@dpaInc , help here please

Answer 2

where is he?

Answer 3

where is who?

Answer 4

u

Answer 5

Ohh:). lol

Answer 6

I am missing VA and zeroes and symmtrey

Answer 7

Is my domain correct in this case?

Answer 8

Also, Is my period correct? If im not wrong the horizontal distance between cycles in this case is pi

Answer 9

i need to reread the question... your function is 1/tanx

Answer 10

Yes

Answer 11

ok. 1/tanx = cotx = cosx/sinx.

Answer 12

Thats right

Answer 13

so your Vasymptotes occur where sinx=0 and that does reflect what you stated in your domain. these are the "except" parts.

Answer 14

Are the zeroes by any chance: ...,-pi/2, pi/2, ...

Answer 15

sorry man i don't know where my head is... cosx/sinx.... your zeros occur where cosx=0...

Answer 16

What would be my cosx?

Answer 17

because if the numerator is cosx. whatever makes the numerator =0 will make cotx = 0.

Answer 18

scratch out "if"

Answer 19

wait, before we solve this. i need to know. Are all of my other properties correct? is my period correct?

Answer 20

from what you have filled in yes...

Answer 21

were working on the ones not filled in right?
• Domain: {All real numbers except all n*pi, for pi is an integer}
• Range: {y | y is an element of R}
• Period: Pi
• Vertical Asymptotes:
• Zeroes:
• Symmetry:
• Y-Intercept: tan(0) = sin(0)/cos(0) = 0

Answer 22

Yes, The ones not filled Im still not sure, But I wanted to know if all the properties I filled are correct

Answer 23

Ok, so i found the \zeroes by graphing it. zeroes are multiples of pi/2

Answer 24

Domain: {All real numbers except all n*pi, for pi is an integer}
pi radian =180 degrees...
So , pi is not an integer. Sorry to interrupt!

Answer 25

how did i miss that?

Answer 26

So what would my domain be then?

Answer 27

do you need it in radian or degree?

Answer 28

for "n" is an integer...

Answer 29

It doesnt specify, but I believe its radian

Answer 30

Im working all of it in Radian

Answer 31

Okay, Domain: {All real numbers except all n*pi, for n is an integer}
-> Cool~ Owl with a black hat :)

Answer 32

So my domain is correct then?

Answer 33

correct ''for pi is an integer'' to '' for n is an integer''

Answer 34

Oh ok.

Answer 35

How about my period? is it correct?

Answer 36

y3es

Answer 37

period is correct

Answer 38

Awesome.

Answer 39

(Big clap!!!)

Answer 40

Ok so for zeroes I got ...-pi/2, pi/2,… . The zeroes are all multiples of pi/2.

Answer 41

This can be proven when graphing the function. The lines cross in the multiples of pi/2 in the x-axis

Answer 42

you can also write it the way you did with the domain: n*pi + pi/2, where n is an integer.

Answer 43

Did I solve my yintercept correctly?

Answer 44

yes. symmetry?

Answer 45

Symmetry i have NO idea:(

Answer 46

try this cot(-pi/4) and compare that with cot(pi/4)

Answer 47

The give me opposite values. -1 and 1

Answer 48

do you know what that means?

Answer 49

Cot(-pi/4) gives me -1 and the other gives me1

Answer 50

Hmm.. I really doubt if there is an y-intercept :S
I should be undefined...., a vertical asymptote there!!

Answer 51

really? i'm glad Callisto's here, don't you?

Answer 52

1/tanx = cosx/sinx
Put x=0
y = cos 0 /sin 0 = 1/0 = undefined

Answer 53

Yeah! Im glad both of you are here!

Answer 54

i keep referring to tanx and not cotx. sorry again....
but that does not change the question about symmetry

Answer 55

You are right! It doesnt cross in the y-axis, so it is undefined! thanks for catching that

Answer 56

Ok, is the VA: 0, pi, and multiples of pi

Answer 57

I think so...If I'm not wrong :(

Answer 58

Ok, symmetry I have trouble with

Answer 59

do you remember that question you answered earlier about cot(-pi/4) and cot(pi/4) and you told me 1 and -1?

Answer 60

Yes, What does that mean?

Answer 61

I understand the relationship, but how do I explain it

Answer 62

ok... do 1 more for me... cot(-pi/3) = cot(pi/3)

Answer 63

what relationship is that?

Answer 64

Same thing, -0.5 and 0.5

Answer 65

Does it mean that the symmetry is rotational?

Answer 66

correct you're getting the opposite y value when you stick in a negative x value... do you know what that's called?

Answer 67

whoa... you're too fast for me again...

Answer 68

yes. specifically this function is an odd function... rotationally symmetric.

Answer 69

Zeroes: ...-pi/2, pi/2,… . The zeroes are all multiples of pi/2.
Seems not really... pi is a multiple of pi/2 (2 x pi/2) but it's not 0...

Answer 70

she's right... again....:)

Answer 71

But when tracing the zeroes, all of the lines crossed in the multiples of pi/2 in the x-axis

Answer 72

That is how we trace the zeroes, and when graphed, that is where all the zeroes were located

Answer 73

but what you have in your answer includes pi...

Answer 74

there are asymptotes there.

Answer 75

Ohhh. so is my VA wrong or is my zero wrong?

Answer 76

zero

Answer 77

Oh boy

Answer 78

Zeroes: ...-pi/2, pi/2,… . The zeroes are all multiples of pi/2, that is n* pi/2 , where n is an odd integer. Perhaps that's better? Sorry my limited English :(

Answer 79

So like this right?

...-pi/2, pi/2,. The zeroes are all multiples of pi/2, that is n* pi/2 , where n is an odd integer

Answer 80

Ok, so with that fixed, are my other properties ok?

Answer 81

...-pi/2, pi/2,. The zeroes are all odd multiples of pi/2, that is n* pi/2 , where n is an odd integer
@dpaInc Does that look good to you?

Answer 82

looks good to me... and everything else too.

Answer 83

Awesome! Can you double check one more for me? Sorry to bother you guys so much

Answer 84

i'll double check if you do this problem for me...