- cutiecomittee123

What functions are equivelent to y=4cosx-2
y=4cos(-x)-2
y=4sin(x+pi/2)-2
y=4sin(x-pi/2)-2
y=-4cosx+2

- katieb

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- jango_IN_DTOWN

cos(-x)=cos x . now try

- imqwerty

these are some identities try using them to get the answer
\[\cos(-x)=\cos(x)\]\[\sin \left( \frac{ \pi }{ 2 }+x \right)=\sin(x)\]\[\sin \left( \frac{ \pi }{ 2 }-x \right)=\cos(x)\]

- cutiecomittee123

so a and d work in that case?

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## More answers

- imqwerty

d won't work

- cutiecomittee123

how so?

- cutiecomittee123

is it because its not the x that is being negative, its the whole equation?

- cutiecomittee123

and is that the only one that is equal?

- imqwerty

so if d is the answer
-4cos(x)+2=4cos(x)-2
bring both on right hand side
0=8cos(x)-4
is this correct
no its not so d won't wrk
what do u think about c

- cutiecomittee123

oh i see, so if you just set them equal to eachother and solve then you will get your answers!!!!!

- imqwerty

yea u can check the options like that

- imqwerty

if the option u choose satisfies the equation then its correct :D

- cutiecomittee123

cool thanks

- jim_thompson5910

You can also use a graphing calculator to check.
https://www.desmos.com/calculator/lwlzconupi
Notice how the original graph of `y=4cos(x)-2` (in red) does not match with choice D `y=-4cos(x)+2` (in blue). If they did match, then one curve would be right on top of the other. You can turn on/off the graphs to see if one was on top of the other.

- jim_thompson5910

this shows how the original graph matches up with choice A
https://www.desmos.com/calculator/gwwpecq6te
click the circle icons to turn the graph on/off and you'll see one graph overlapping perfectly on the other

- cutiecomittee123

well b and c cannot match because they are sin and the origional is cosine, right?

- cutiecomittee123

actually i just tested it and b actually matches up

- jim_thompson5910

btw @imqwerty it should be sin(pi/2 + x) = cos(x)

- cutiecomittee123

https://www.desmos.com/calculator/lwlzconupi

- jim_thompson5910

yeah B should match with the original

- cutiecomittee123

so b and d are both equal

- imqwerty

>.< oh srry silly mistake

- jim_thompson5910

`so b and d are both equal` incorrect

- cutiecomittee123

yeah but b and d match up

- cutiecomittee123

so then just d? was I right about the fact that they cannot be the same because b and c are sine and the origional is cosine?

- jim_thompson5910

since sin(pi/2 + x) = cos(x), this means y=4sin(x+pi/2)-2 turns into y=4cos(x)-2

- cutiecomittee123

okay i kind of get that so does that mean that c works

- jim_thompson5910

one moment

- cutiecomittee123

i graphed it and they matched up

- jim_thompson5910

ok I graphed the original equation (in box 1) and the four answer choices (boxes 2 through 5). Only box 1 is turned on. The other graphs are turned off
https://www.desmos.com/calculator/koejh8yigm
I recommend going through each and turn them on one at a time.
example: turn on box 1 and box 3 to compare the original with choice B

- jim_thompson5910

hopefully you'll be able to see that
A matches
B matches
C does not match
D does not match

- cutiecomittee123

yep that what i see too. I tested it out

- jim_thompson5910

ok great

- cutiecomittee123

sweet thanks

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