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## cutiecomittee123 one year ago 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

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1. anonymous

cos(-x)=cos x . now try

2. 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)$

3. cutiecomittee123

so a and d work in that case?

4. imqwerty

d won't work

5. cutiecomittee123

how so?

6. cutiecomittee123

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

7. cutiecomittee123

and is that the only one that is equal?

8. 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

9. cutiecomittee123

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

10. imqwerty

yea u can check the options like that

11. imqwerty

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

12. cutiecomittee123

cool thanks

13. 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.

14. 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

15. cutiecomittee123

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

16. cutiecomittee123

actually i just tested it and b actually matches up

17. jim_thompson5910

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

18. cutiecomittee123
19. jim_thompson5910

yeah B should match with the original

20. cutiecomittee123

so b and d are both equal

21. imqwerty

>.< oh srry silly mistake

22. jim_thompson5910

so b and d are both equal incorrect

23. cutiecomittee123

yeah but b and d match up

24. 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?

25. jim_thompson5910

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

26. cutiecomittee123

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

27. jim_thompson5910

one moment

28. cutiecomittee123

i graphed it and they matched up

29. 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

30. jim_thompson5910

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

31. cutiecomittee123

yep that what i see too. I tested it out

32. jim_thompson5910

ok great

33. cutiecomittee123

sweet thanks

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