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

- anonymous

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

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- Thats_Kyy

Hold On Give Me A min Okay?

- anonymous

okay!

- anonymous

good luck

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- anonymous

can you explain that ?? @Albany_Goon

- anonymous

that all i got lemme do sum more digging

- anonymous

okay

- freckles

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

- anonymous

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

- 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

- freckles

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

- freckles

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

- anonymous

no i dont

- 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

- 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?

- anonymous

3pi/2?

- 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

- freckles

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

- anonymous

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

- 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

- freckles

this will isolate the x

- anonymous

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

- freckles

sure

- anonymous

okay give me a minute please

- freckles

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

- freckles

been having some internet issues with my provider :(

- anonymous

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

- anonymous

and its fine i do to

- 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

- anonymous

gotcha! thank you so much!!!

- freckles

np

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