Question

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

Answer 1

Hold On Give Me A min Okay?

Answer 2

okay!

Answer 3

good luck

Answer 4

can you explain that ?? @Albany_Goon

Answer 5

that all i got lemme do sum more digging

Answer 6

okay

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

no i dont

Answer 13

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

Answer 14

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?

Answer 15

3pi/2?

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

this will isolate the x

Answer 21

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

Answer 22

sure

Answer 23

okay give me a minute please

Answer 24

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

Answer 25

been having some internet issues with my provider :(

Answer 26

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

Answer 27

and its fine i do to

Answer 28

\[4x=\frac{\pi}{2}+2 \pi n \text{ or } 4x=\frac{3\pi}{2}+2 \pi n \\ \text{ multiply both sides by } \frac{1}{4} \\ x=\frac{\pi}{2(4)}+\frac{2 \pi n}{4} \text{ or } x=\frac{3 \pi}{2(4)}+\frac{2 \pi n}{4} \\ \text{ simplifying } \\ x=\frac{\pi}{8}+\frac{\pi n}{2} \text{ or } x=\frac{3\pi}{8}+ \frac{\pi n }{2}\]


note:
since 2/4=1/2

Answer 29

gotcha! thank you so much!!!

Answer 30

np