roselin 2 years ago explain why the equation cox=x has at least one solution.

1. zepdrix

cox???

2. roselin

sorry,sorry. its cos x

3. zepdrix

oh lol ^^

4. zepdrix

Hmm do you remember what the graph for cosine looks like?

5. roselin

somewhat

6. baldymcgee6

I'm pretty sure cos(x) = x only has one solution

7. baldymcgee6
8. zepdrix

|dw:1351373928927:dw| This is kind of the idea rose :D At this particular point, the x value and the cosx value are the same.

9. roselin

|dw:1351373944681:dw|

10. zepdrix

So in your picture, x=pi/2 but cosx = 0 Hmm that point doesn't work so well :c

11. roselin

okay, i will consider the picture that you showed

12. zepdrix

Yah I can't think of the proper way to explain it :D It probably has something to do with the fact that cosine oscillates back and forth between 1 and -1, and since it is continuous it would have to have a solution :d i dunno... just think about it i guess :3 heh

13. baldymcgee6

Since the function y = x has a domain of all real numbers... as is cos(x), there must be a point of intersection somewhere

14. roselin

okay,

15. roselin

So which one should I consider now? i have two answers here

16. baldymcgee6

Combine them... you could say.. Since both y=x and the cosine function have a domain of all real numbers and both are continuous at least one point of intersection is definite.

17. roselin

oh okay, thank you so much guys

18. Zarkon

use the intermediate value theorem

19. latremese40

roelin i think you did it right