Question

Can someone help me find the domain and range of y=3csc(3x+pi)-2 ?

Answer 1

https://www.google.com/search?q=y%3D3csc(3x%2Bpi)-2+%3F&oq=y%3D3csc(3x%2Bpi)-2+%3F&aqs=chrome..69i57&sourceid=chrome&es_sm=122&ie=UTF-8

Answer 2

idk because Im in 7th grade...

Answer 3

@ganeshie8 Can you help me with this math problem?

Answer 4

@e.mccormick @thomaster Can you help me with this math problem? (AP Calculus, Trig review)

Answer 5

I know that the domain is supposed to be kpi/3, but I don't know how to get that.

Answer 6

@e.mccormick

Answer 7

@thomaster

Answer 8

@amistre64 @ganeshie8 Can you help me?

Answer 9

the csc function rides on the humps of which function?

Answer 10

whenever the function is rides on goes zero, the inverse hits a divide by zero and we eliminate those from the domain

Answer 11

the 'parent' functions range llives between a min and max, the inverse hits everything else everything else

Answer 12

in other words, exploring the parent function will help us determine this one

Answer 13

@amistre64 so how do I do that to find the domain?

Answer 14

what is the 'parent' function that csc is an inverse of?

Answer 15

y=sin x ?

Answer 16

inverse is a bad name for it in trig .... reciprocal

and yes, sin of whtever argument they used

Answer 17

now, there is only one real number that doesnt have a good reciprocal: 0

if we flip it we get n/0 soo ... we need to exclude every argument that makes sin go zero

Answer 18

How do I find what makes sin zero?

Answer 19

um, that is going to be one of those basic trig questions that you should have in memory already

Answer 20

sin(u) = 0

then solve the argument they give you to equate it to u

Answer 21

What is u?

Answer 22

u is an argument that we can use that is not x ....

Answer 23

I feel like I should know all of this, but I don't remember learning it. The textbook doesn't say anything about it either.

Answer 24

when does sin equal zero? you need to know this, ill correct you if need be but i cant just tell you outright

Answer 25

You mean on the unit circle?

Answer 26

i cant draw at the moment or id demonstrate a unit circle

Answer 27

yeah

Answer 28

Everyone else online was saying you have to solve for sin (3x+ pi) = k pi or something like that so maybe that's confusing me but I'm not sure.

Answer 29

itll be more like, find when sin(u) = 0

then u = 3x+pi will solve for x

(u - pi)/3 = x

Answer 30

I'm pretty sure its zero at 0 and pi

Answer 31

0 and pi are good, but aslo 2pi, 3pi, 4pi .... every integer multiple of pi makes sin go zero

Answer 32

so, lets say u = k pi, such that k is an integer

Answer 33

okay

Answer 34

so, solving for x, as i already did

(k pi-pi)/3 = x has to be excluded from the set of Real numbers and that defines our domain

Answer 35

(k-1)pi/3 but since k is an integer, then k-1 is also any integer

lets say every k pi/3 for brevity

Answer 36

\[D=\{x \in R:x\ne k\frac{\pi}{3}, k\in Z\}\]

Answer 37

now the range is simple enough, at least for me since i already know my trig :) its the center line, plus/minus the amplitude

Answer 38

(-infinity, -5) U (1, infinity) ?

Answer 39

include the -5 and 1

Answer 40

sin=csc at the humps

Answer 41

What do you mean by include

Answer 42

your notation, when we want to omit an endpoint we close it with ) when we want to include it, it EQUALS it, we draw an equal sign connected by a bar: ]

Answer 43

since infinity can never be equated, you use ( and ) which is fine,

but -5 and 1 are PART of the range and need to be included since we can equal -5 or 1

Answer 44

Oh okay so just use brackets instead of parentheses?

Answer 45

for the -5 and 1 yes

Answer 46

ok thank you. There's another problem like this but it uses tangent instead of csc. Do you think you could help me out on that as well?

Answer 47

tangent is a common trig function, its built out of sin and cos:

tan = sin/cos

so when do you think we would omit a part of the domain?

Answer 48

At pi/2 and 3pi/2?

Answer 49

That's when cot is zero I believe

Answer 50

odd integer multiples of pi/2 yep

Answer 51

the equation is
y = -3 tan (2x + pi) + 2

Answer 52

Not sure what to do next..

Answer 53

oops I meant
y = -3 tan (3x + pi) + 2

Answer 54

3x + pi = kpi/2 ?

Answer 55

I'll take that as a yes..