How do you graph r=12/(-4costheta+6sintheta)r=124cosθ+6sinθ?

2 Answers
Mar 22, 2018

Draw a line with a yy-intercept of 22 and a gradient of 2/323

Explanation:

Multiply each term by (-4costheta+6sintheta)(4cosθ+6sinθ)

r(-4costheta+6sintheta)=12r(4cosθ+6sinθ)=12

-4rcostheta+6rsintheta=124rcosθ+6rsinθ=12

-2rcostheta+3rsintheta=62rcosθ+3rsinθ=6

rcostheta=xrcosθ=x
rsintheta=yrsinθ=y

-2x+3y=62x+3y=6
y=(2x+6)/3=(2x)/3+2y=2x+63=2x3+2

Draw a line with a yy-intercept of 22 and a gradient of 2/323

Mar 22, 2018

I use the Desmos Graphing Calculator; it is a free online graphing tool that anyone can use.

Explanation:

One thing that I do not like about the calculator is that it requires that polar equations be in the form r = f(theta)r=f(θ); it will graph your equation very well but it will not graph something like the following:

r^2 = r sin(theta) + 5r2=rsin(θ)+5

It does not have this requirement for Cartesian equations.

I like that you can graph multiple equations and you can select the colors that you like.

I wish that it did 3d plots but you can't have everything for free.

You can make a user-id and I have one but I found that you have all of the features except the ability to save your work without logging on.