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anonymous
 one year ago
Transform each polar equation to an equation in rectangular coordinates and identify its shape.
a. θ = (π / 6)
b. r = (4 / (2cosθ  3sinθ))
anonymous
 one year ago
Transform each polar equation to an equation in rectangular coordinates and identify its shape. a. θ = (π / 6) b. r = (4 / (2cosθ  3sinθ))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 @freckles @Luigi0210 @radar @rvc @sleepyjess

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think for A, r = 2 but I'm not sure

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\theta=\frac{\pi}{6}\] actually describes a line dw:1433651567694:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4so you know your line will be of the form y=mx

freckles
 one year ago
Best ResponseYou've already chosen the best response.4now the job is to find m

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\text{ recall } \frac{y}{x}=\tan(\theta) \\\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4plug in your value of theta

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you can also write that as y=tan(theta)*x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought we were finding m? Are we going backwards now?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4m is just a constant value I showed what m was by replacing m with tan(theta) and I got m was tan(theta) by using the equation y/x=tan(theta)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh, so how do I find out what x and y are since I already know theta?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4I knew my equation would look like this because I knew theta=a number is a line \[y=mx\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4y and x are variables

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you only need to find m aka tan(theta)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But I already know what theta is for a. I need to know how to find r, right?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1You don't need to find r

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then how am I supposed to graph it, if I don't know what r is?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1You just need to find the Cartesian form of the polar equation \(\theta = \frac{\pi}{6}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay...how do I do that?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1You know that's a straight line, right?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Do you know how to get a equation of a line?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1you know the Cartesian form of the line is y=mx+c, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so how would I write that with pi/6??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hello...??? @amilapsn

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Calm down... @Shorty1234 take a deep breath.... :)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1yes of course.... You have to find m and c... what would be c, (it's easy)?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1No... I'll ask again... you know the Cartesian form of the line is y=mx+c, right? What would m and c represent?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0m is the slop and c is the yintercept

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1yes that's it what's the y intercept =c then?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1What do you mean by the y intercept?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that not what "c" represents ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay...so whats your point

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1y intercept is the y coordinate where straight line cuts the y axis, right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4sorry lost internet connection do you remember the drawing I made (since you guys are talking about the yintercept)dw:1433653769876:dw where does that cross the yaxis?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it doesnt...so is it zero?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4well it does at 0 (0 is a number :)) so that is how I got y=mx earlier

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to find m right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so my answer for a would be (0, pi/6)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4anyways I will let @amilapsn continue since I was gone so long

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.....is there more stuff I have to do??

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1you do have to find m, right?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1can you tell me the relation ship between  pi/6 and slope?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1That's it! So m would be..............?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433654449002:dw I'm sorry I said I was going to stay away :p but can you replace pi/6 and x and y using any trig ratio?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4by the way that is a right triangle I made there

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1no.... Can you tell me the relationship between m and pi/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I give up, this makes zero sense

freckles
 one year ago
Best ResponseYou've already chosen the best response.4do you know tan(theta)=opp/adj?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433654806812:dw so tan(pi/6)=?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1......in terms of y and x?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4yes using the right triangle above

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1can you express the same in terms of x and y ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand???

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1using the right triangle drawn by freckles...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i don't know what x is?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1yes you don't indeed... use just x and y...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so express x and y using x and y? that makes no sense

freckles
 one year ago
Best ResponseYou've already chosen the best response.4no express tan(pi/6) in terms of x and y

freckles
 one year ago
Best ResponseYou've already chosen the best response.4using the right triangle

freckles
 one year ago
Best ResponseYou've already chosen the best response.4I have even labeled the opposite side with the correct measurement and the adjacent side too for the point (x,y)

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433655304381:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4where opp is y and adj is x right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4so can you say what tan(pi/6)=? in terms of x and y now?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you forgot the x on denominator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so tan(pi/6) / x = y?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4:( tan(theta)=y/x you know what theta is just plug in your theta

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you are making this way complication your Cartesian equation is suppose to be in terms of y and x you know theta=pi/6 so you will have an equation in terms of x and y if you replace the theta with pi/6

freckles
 one year ago
Best ResponseYou've already chosen the best response.4lol i'm having trouble with english tonight :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.....this makes no sense

freckles
 one year ago
Best ResponseYou've already chosen the best response.4why ? I thought the visual made it pretty clear

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433655836599:dw if this point is (x,y) then ...

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433655860761:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4tan(pi/6)=opp/adj where opp=y and adj=x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, I dont get this...

freckles
 one year ago
Best ResponseYou've already chosen the best response.4let me just do an example I guess say we have \[\theta=\frac{\pi}{4}\] again this is a line going through the origin this is of the form y=mx we only need to determine m we can draw this line dw:1433655974295:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4let's say point (x,y) is somewhere on there randomlydw:1433656006691:dw just choose a spot

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433656020961:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4well looking at this triangle I can make the observation that \[\tan(\frac{\pi}{4})=\frac{y}{x} \] I can be done here

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[1=\frac{y}{x} \\ \text{ I can also multiply } x \text{ on both sides } y=x\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4y=x is the Cartesian (aka rectangular form ) of the polar equation theta=pi/4

freckles
 one year ago
Best ResponseYou've already chosen the best response.4say we have theta=pi/4 well that would just be tan(pi/4)=y/x which is 1=y/x which isx=y

freckles
 one year ago
Best ResponseYou've already chosen the best response.4say we have theta=pi/3 that would just be tan(pi/3)=y/x or y=tan(pi/3)x we can evaluate tan(pi/3) \[\tan(\frac{\pi}{3})=\frac{\sqrt{3}}{1}=\sqrt{3}\] so theta=pi/3 can be written as the Cartesian equation \[y=\sqrt{3}x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So my answer would be y = tan(pi/6)x ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4yes and simplify the tan(pi/6)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right,I'll do that. So what about the second problem. Hopefully it what take as long to figure out....

freckles
 one year ago
Best ResponseYou've already chosen the best response.4b. r = (4 / (2cosθ  3sinθ)) multiply both sides by the denominator on right hand side you will need the other two equations to help you to convert this in terms of x and y that you will need rcos(theta)=x and rsin(theta)=y

freckles
 one year ago
Best ResponseYou've already chosen the best response.4by the way these equations are useful when converting from one to the other \[r^2=x^2+y^2 \\ \tan(\theta)=\frac{y}{x} \\ x=r \cos(\theta) \\ y=r \sin(\theta)\] these are your tools to work these particular puzzles

freckles
 one year ago
Best ResponseYou've already chosen the best response.4though it is kinda useful knowing why they are and that is why I drew the picture above because it doesn't appear you know why these equations are

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1433657166077:dw all of those equations can be found just by using this picture

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433657937284:dw

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Things may seem complicated... But they aren't..! Math is the way to sort things out!! :)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Hope is the only thing you should have!!

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1Don't give up.. Just try....!

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1You'll find the mathematician inside you..

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433658575750:dw
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