## anonymous one year ago *FAN AND MEDAL* help with Where are the asymptotes of f(x) = tan 4x from x = 0 to x =?

1. Thats_Kyy

Hold On Give Me A min Okay?

2. anonymous

okay!

3. anonymous

good luck

4. anonymous

can you explain that ?? @Albany_Goon

5. anonymous

that all i got lemme do sum more digging

6. anonymous

okay

7. freckles

I don't understand why all of your questions end in to x=?

8. anonymous

i dont know either! theyre practice questions and im trying to review but ive never answered ones that end with x=?

9. freckles

anyways tan(4x)=sin(4x)/cos(4x) you just need to find when the bottom is 0 that is solve cos(4x)=0 for x

10. freckles

this will give you the vertical asymptotes of the graph of f(x)=tan(4x)

11. freckles

$\cos(4x)=0 \\ \\ \text{ I guess we will just find them all } \\ \text{ first do you know how to solve } \\ \cos(u)=0$

12. anonymous

no i dont

13. freckles

can you look on the unit circle and know for which angles the x coordinates are 0 http://managementscience.biz/wp-content/uploads/2014/10/unit-circle.gif

14. freckles

I will tell you one angle at 90 deg I see we have the x-coordinate is 0 so u=pi/2 rad is an answer to cos(u)=0 can you give another from looking at that picture?

15. anonymous

3pi/2?

16. freckles

awesome! so we have the solutions to: $\cos(u)=0 \text{ are } u=\frac{\pi}{2}+2\pi n \text{ or } u=\frac{3\pi}{2}+2 \pi n \\ \text{ but we wanted to solve} \\ \cos(4x)=0 \\ \text{ well this equation is exactly the same as the one before except we had } \\ u \text{ instead of } 4x \\ \text{ just replace the } u's \text{ in the first equation } \\ \text{ with } 4x \\ \text{ that is you should have } \\ \cos(4x)=0 \text{ has solutions given by } \\ 4x=\frac{\pi}{2}+2 \pi n \text{ or } 4x=\frac{3\pi}{2}+2 \pi n \\$ oh and n is an integer

17. freckles

you can finish solving for x by multiplying both sides by 1/4

18. anonymous

and then whatever i get after solving for x will be the asymptotes?

19. freckles

yep but make sure you leave the x in you know the asymptote should be written as an equation not just a value that is your answer should be x=something just take the equations I have given you and multiply both sides by 1/4

20. freckles

this will isolate the x

21. anonymous

can i do it and then you tell me if i get it right?

22. freckles

sure

23. anonymous

okay give me a minute please

24. freckles

ok I will be here as long as my internet doesn't mess up like it did earlier :p

25. freckles

been having some internet issues with my provider :(

26. anonymous

how do you multiply 1/4 times $2\pi n$

27. anonymous

and its fine i do to

28. freckles

$4x=\frac{\pi}{2}+2 \pi n \text{ or } 4x=\frac{3\pi}{2}+2 \pi n \\ \text{ multiply both sides by } \frac{1}{4} \\ x=\frac{\pi}{2(4)}+\frac{2 \pi n}{4} \text{ or } x=\frac{3 \pi}{2(4)}+\frac{2 \pi n}{4} \\ \text{ simplifying } \\ x=\frac{\pi}{8}+\frac{\pi n}{2} \text{ or } x=\frac{3\pi}{8}+ \frac{\pi n }{2}$ note: since 2/4=1/2

29. anonymous

gotcha! thank you so much!!!

30. freckles

np

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