# how do u sketch those graphs......... (1 Viewer)

#### Hikari Clover

##### Member

please sketch the inverse relation for this function......

i heard some1 says the trick to draw inverse function is to rotate ur paper somehow, but i dont no exactly......
can any1 tell me if u no the method?

also,how u guys usually start drawing inverse trig function?
u find the domain and range first?
if u r given a graph like above, how do u skecth its inverse cos, tan etc.....

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OABC is a square. O represents the complex 0
A represents the complex NO. 3+i, B represents a complex number z and C represents the complex NO. w
D is the point of the intersection of the diagonals.
i) find the complex numbers corresponding to points C and D in the form x+iy
ii) find arg(w/z)
iii) if E is the fourth vertex of the parallelogram OAEB find the complex number corresponding to E….

just wondering the last bit,(iii) ,how many points would u find for E?
isn't it the square itself a parallelogram,so E could be at C?

thx:wave:

#### yummaypho

##### New Member
heya another way to draw the inverse i heard was to fold the paper on the line y=x
and just draw a mirror image of it. jsut get like a light texta and plot it

lol good idea

#### Yip

##### Member
here is a cheap way of drawing inverses:
by definition, if u have a function like y=x^2, in the inverse, u just swap the ys and xs to get x=y^2
Therefore, just swap the x and y labels on ur axis so ur x becomes the vertical axis and y is the horizontal. Then, to appease the marker, just rotate it so that it looks normal again, though i see no reason why having the x as a vertical axis is "wrong", just non-standard lol

#### victorheaven

##### Member
u cant have an inverse function with this one as its not one-to-one.

#### nubix

##### Member
I usually rotate the paper about 45° CCW, draw the line y=x and use that as an axis of symmetry; whatever's on the right I flip to the left and vice versa.

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#### littlemaster

##### Member
yeah thats true its not monotonic, hence fails the horizontal line test.

they must have speccified a domain.

I draw f(x):
-flip the piece of paper, rotate it 90 degrees clockwise. and there you have it.

just make sure u use a dark pen!

#### Chinmoku03

##### Ippen, Shin de Miru?
Yeah, like everyone else said, f(x) isn't a one one function, so unless there's a given domain, there's no inverse.

As for the complex number question, your idea sounds right IMO. Maybe just find w to be safe. Then again, I'm crap at complex, so yeah >.>;

#### Hikari Clover

##### Member

littlemaster said:
yeah thats true its not monotonic, hence fails the horizontal line test.

they must have speccified a domain.

I draw f(x):
-flip the piece of paper, rotate it 90 degrees clockwise. and there you have it.

just make sure u use a dark pen!

shouldnt it be 90 degrees anti-clockwise

#### Hikari Clover

##### Member

what u guys do to the inverse trig function?

#### Chinmoku03

##### Ippen, Shin de Miru?
My process:

1) Remember the basic inverse graphs
2) Find the domain and range
3) Sketch

Lol, sounds like how everyone else would do it ^.^;

#### Hikari Clover

##### Member

Chinmoku03 said:
My process:

1) Remember the basic inverse graphs
2) Find the domain and range
3) Sketch

Lol, sounds like how everyone else would do it ^.^;

=.=|||
i would "use calculator to work out some points" b4 i Sketch

how the inverse sin/cos/tan for the graph above look like?

#### elseany

##### Member
a good way is to draw your y = x line and place your ruler along it so its standing perpendicular to the sheet, that way you can see the reflection of your curve in the ruler and then use that as a guide to draw the mirror of it

the other way is heaps easier but takes a while, you draw your graph, flip over your peice of paper, trace the graph through the paper and switch the labels of the axes.

#### littlemaster

##### Member
Re: 回复: Re: how do u sketch those graphs.........

Hikari Clover said:
shouldnt it be 90 degrees anti-clockwise

clockwise works for me.....

i flip the page to the left tho...give it a go, you can always resort to the other methods they are much more efficient.