## anonymous one year ago In the function f(x) = sec 2x, what are the following: - Domain - Asymptotes

1. SolomonZelman

Domain will have gaps. $$f(x)=\sec^2(x)$$ $$f(x)=\displaystyle \frac{1}{ \cos^2(x)}$$ so for every value where cos²(x)=0, you have a vertical asymptote.

2. anonymous

Wait, so $\sec^2x$ is also $\sec2x$?

3. anonymous

Can I use the T-table to graph the function or nah?

4. SolomonZelman

Also, you know that |cos x| < |sec x| And cos(x) (as well as sine), is between 1 and -1. This way, |sec x| is always ≥1 and ≤-1. So, it will look roughly like this: |dw:1437070613045:dw|

5. anonymous

Also, is there any way to find the domain without graphing?

6. SolomonZelman

wait, I thought you didn't use a caret (^), but your function is sec(2x)?

7. anonymous

Yup it is sec(2x).

8. SolomonZelman

So, it will be same as sec²x still. JUST THAT: the arcs will be thinner. the asymptote is everywhere when cos(x)=0

9. SolomonZelman

But it is still same, because if cos(x)=0, then cos²(x)=0 as well./

10. anonymous

Yes, that's why the range is $(-\infty, -1], [1,\infty)$ correct?

11. SolomonZelman

yes

12. SolomonZelman

((With a U in the middle ))

13. SolomonZelman

(-∞,-1] U [1,∞)

14. anonymous

oh yeah right. I thought you said no haha.

15. anonymous

So the period is pi.

16. anonymous

And there is no amplitude, right?

17. SolomonZelman

yes, period is π

18. SolomonZelman

yes no amplitude.

19. SolomonZelman

(I am lagging, my connection is bad)

20. anonymous

So the domain is all real nos. except ±π/4, ±3π/4, ±5π/4

21. SolomonZelman

yes$$\color{red}{,}$$ no amplitude. (like that)

22. SolomonZelman

yes, and so on.... for all values tof x, that make cos(x)=0

23. SolomonZelman

of* x

24. anonymous

Also, in the book, it says the domain is all real nos except $\frac{ \pi }{ 2}+\pi n$

25. anonymous

What does it mean? Is it the same with what I stated above?

26. SolomonZelman

for all integer values of n.... that is the pattern in which these numbers are generated

27. SolomonZelman

i need to refresh. sorry. hold on.

28. anonymous

Okay, so how do I put the domain like that?

29. SolomonZelman

well, you can say that same thing in the book, and don't forget to add that $${n \in {\bf Z}$$

30. SolomonZelman

ops

31. SolomonZelman

So, you can state (for the asymptotes) that $$\large\color{black}{ \displaystyle \frac{\pi }{2} +\pi\cdot n;~\left\{n \in {\bf Z} \right\} }$$

32. anonymous

|dw:1437071434398:dw|

33. SolomonZelman

you can use wolframalpha.com to fill in the table.

34. SolomonZelman

it is a very cool calculator.

35. anonymous

No, I don't want just the answers.

36. SolomonZelman

What do you want then?

37. anonymous

I want to learn.

38. SolomonZelman

Oh, I mean not a graphing calc. I mean to find particular values of cse(2x), if you want. Or, you can plug the values yourself, and calculate them yourself. And if you encounter a problem calculating (by hand) one value or the other, you can ask me.

39. anonymous

Yup, I want to plug the values myself.

40. anonymous

The thing is I don't know how to start. I just know that the "count number" is pi/4.

41. anonymous

$\frac{ 1 }{ 4 } \times (period)$

42. SolomonZelman

don't really know what 1/4 • period means

43. anonymous

Okay, so how would I find the x-values then?

44. anonymous

THANK YOU FOR THE HUGE HELP @SolomonZelman !

45. anonymous

oops didn't mean to use uppercase lol

46. anonymous

Domain: all real numbers other than: ±π/4, ±3π/4, ±5π/4... Range:(-∞,-1) U (1,∞) Period: π Asymptotes:x=±π/4, x=±3π/4, x=±5π/4...

47. pooja195

yes and?

48. pooja195