## anonymous one year ago Graph the function in the interval from 0 to 2pi

1. anonymous

2. anonymous

@UsukiDoll

3. anonymous

@satellite73

4. anonymous

@oleg3321

5. Oleg3321

ehh idk how to do this one :( sorry

6. anonymous

Ok thanks :)

7. anonymous

@Michele_Laino

8. anonymous

9. anonymous

10. anonymous

11. anonymous

12. anonymous

Are my options

13. Michele_Laino

we can rewrite your function as follows: $y - 2 = 2\cos \left( {x + \frac{\pi }{6}} \right)$

14. anonymous

how do we graph it from there?

15. Michele_Laino

now I make this traslation of the x,y-plane: $\left\{ \begin{gathered} Y = y - 2 \hfill \\ X = x + \frac{\pi }{6} \hfill \\ \end{gathered} \right.$ where X and Y are the new coordinates

16. Michele_Laino

using those coordintes, we can rewrite your function as below: $Y = 2\cos X$

17. Michele_Laino

am I right?

18. anonymous

I think so. Which graph would work best?

19. Michele_Laino

the graph of the function: $Y = 2\cos X$ is: |dw:1436508552379:dw|

20. anonymous

Do you think graph B is the best fit?

21. Michele_Laino

now we have to refer that graphys to our old coordinates x,y

22. Michele_Laino

graphic*

23. Michele_Laino

in order to do that, we note that the origin of the X,Y plane is located at: X=0, and Y=0 so substituting into our transformation formulas, we get: $\left\{ \begin{gathered} 0 = y - 2 \hfill \\ 0 = x + \frac{\pi }{6} \hfill \\ \end{gathered} \right. \Rightarrow \left\{ \begin{gathered} y = 2 \hfill \\ x = - \frac{\pi }{6} \hfill \\ \end{gathered} \right.$

24. anonymous

How do i graph that

25. Michele_Laino

so here is the requested graph: |dw:1436508973906:dw|

26. anonymous

i dont have a graph that matches that

27. Michele_Laino

more precisely, we have: |dw:1436509257926:dw|

28. Michele_Laino

yes, you have, please look at the third option

29. Michele_Laino

now you have to neglect the X,Y reference system of my drawing. What do you get?