Finding tangent lines at the pole of 4 = -sin(5theta) | Mathematics | Page 1

charred echo Jul 25, 2023, 2:15 AM

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Polar coords? This is what it looks like

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Poles is unfortunate notation i reckon cuz usually it means a limit to infinity on C

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The tangent lines at the "poles" is prob just this

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Ill give you a hint those are the points at which r is not changing for small changes in theta.

hallow geyser Jul 25, 2023, 2:22 AM

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okay so

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I tried plugging that r into the two x and y equations
which were
x = rcos(theta)
y = rsin(theta)
but like when i do that and find dy/dx, then theres this big fraction that i cant really deal with

charred echo Jul 25, 2023, 2:22 AM

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Don't bother converting just work in polar coords

hallow geyser Jul 25, 2023, 2:22 AM

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oh

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i dont think ive learned how to deal with it in polar coords yet

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it was either that or i set r = 0

charred echo Jul 25, 2023, 2:23 AM

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Just treat theta and r like any other variables

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Differentiate r wrt theta and set it to 0

hallow geyser Jul 25, 2023, 2:24 AM

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differentiate it?

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oh

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can i ask the reason why

charred echo Jul 25, 2023, 2:24 AM

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charred echo Ill give you a hint those are the points at which r is not changing for small ch...

This

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The "poles" are the points where $\frac{d r}{d \theta}=0$

fringe fieldBOT Jul 25, 2023, 2:25 AM

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borisbingobongo

hallow geyser Jul 25, 2023, 2:25 AM

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ohhh

charred echo Jul 25, 2023, 2:26 AM

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After you have the points i reckon you can get the tangent line yourself just some geometry

hallow geyser Jul 25, 2023, 2:26 AM

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so i get -5cos5theta

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and then i set that to 0

charred echo Jul 25, 2023, 2:27 AM

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Yup you'll get an infinite set of repeating theta just pick the ones in range of 0 to 2pi

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Use that to find r values and you've got your points

hallow geyser Jul 25, 2023, 2:27 AM

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is that how i find all the tangent lines

charred echo Jul 25, 2023, 2:28 AM

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Thats how you find the point at which the line has to be tangent

hallow geyser Jul 25, 2023, 2:29 AM

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okay so im not allowed to use a calculator and i get the theta values that arent on the unit circle

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so idk how im supposed to write an answer

charred echo Jul 25, 2023, 2:30 AM

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You shouldn't need a calculator

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-5cos(5x)=0
=>cos(5x)=0
=> What about the nature of 5x

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You know where the zeros of the cosine function are

hallow geyser Jul 25, 2023, 2:33 AM

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yes

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pi/2 and 3pi/2

charred echo Jul 25, 2023, 2:34 AM

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Yes so just pick that first point pi/2

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Now after every multiple of pi you get another zero

hallow geyser Jul 25, 2023, 2:34 AM

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mhm

charred echo Jul 25, 2023, 2:34 AM

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So in general all the zeros of cos function are of the form pi/2+n pi

charred echo Jul 25, 2023, 2:35 AM

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charred echo -5cos(5x)=0 =>cos(5x)=0 => What about the nature of 5x

Equate that with this find a formula for the zeros of cos(5x)

hallow geyser Jul 25, 2023, 2:35 AM

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yea

charred echo Jul 25, 2023, 2:35 AM

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5x=pi/2+n pi

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Now re arrange and just take 5 of the values of x which lie in the 0 to 2pi range the values repeat so just pick what you find easier in this case that'll be the theta terms in 0 to 2pi

hallow geyser Jul 25, 2023, 2:36 AM

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okay

charred echo Jul 25, 2023, 2:37 AM

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Then you'll know at which angles the poles lie. But from your original question given any angle you also know the r magnitude value sooo....

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Find the 5 pole points then I'll leave you to do the tangent lines yourself there are different ways you can approach it so get creative

hallow geyser Jul 25, 2023, 2:39 AM

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alr i'll get to it

#Finding tangent lines at the pole of 4 = -sin(5theta)