Question

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

Answer 1

cos(-x)=cos x . now try

Answer 2

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

Answer 3

so a and d work in that case?

Answer 4

d won't work

Answer 5

how so?

Answer 6

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

Answer 7

and is that the only one that is equal?

Answer 8

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

Answer 9

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

Answer 10

yea u can check the options like that

Answer 11

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

Answer 12

cool thanks

Answer 13

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.

Answer 14

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

Answer 15

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

Answer 16

actually i just tested it and b actually matches up

Answer 17

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

Answer 18

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

Answer 19

yeah B should match with the original

Answer 20

so b and d are both equal

Answer 21

>.< oh srry silly mistake

Answer 22

`so b and d are both equal` incorrect

Answer 23

yeah but b and d match up

Answer 24

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?

Answer 25

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

Answer 26

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

Answer 27

one moment

Answer 28

i graphed it and they matched up

Answer 29

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

Answer 30

hopefully you'll be able to see that

A matches
B matches
C does not match
D does not match

Answer 31

yep that what i see too. I tested it out

Answer 32

ok great

Answer 33

sweet thanks