Cartesian Coordinate

[karatekid_81]

Can someone walk me through this: I have no clue how to do it, I am stuck. I have the solutions manual but it just shows the answer and I would like to see a step by step to get there, thanks in advance.

find the equation of the tangent line in Cartesian coordinates of the curve given in polar coordinates by

r=3-2cos(theta), at theta=pi/2

 

[galactus]

You can find where your line crosses the y-axis (b in y=mx+b) by plugging pi/2 into r.

The tricky part is the slope.

\(\displaystyle \L\\\frac{dy}{dx}=\frac{rcos({\theta})+sin({\theta})\frac{dr}{d{\theta}}}{-rsin({\theta})+cos({\theta})\frac{dr}{d{\theta}}}\)

Plug Pi/2 into your slope and you have it.

As an extra tip, \(\displaystyle \L\\\frac{dr}{d{\theta}}=2sin({\theta})\)

 

[karatekid_81]

I am still stuck I cant figure it out still, dont know where to go from there

 

[stapel]

I am still stuck I cant figure it out still, dont know where to go from there

If you have no idea how to proceed on this, then you might need to have a serious talk with your instructor. You should have at least some idea what's going on here, and, unfortunately, we simply cannot re-teach the necessary background material here. Sorry.

Eliz.

 

[karatekid_81]

I appreciate the help but I just need a walkthrough of one problem. If I can see it all together I am able to see what I am messing up.

 

[stapel]

I appreciate the help but I just need a walkthrough of one problem. If I can see it all together I am able to see what I am messing up.

But... You were given a "walk-through" of "the tricky part", in addition to a picture. You were also told the (algebra) steps to take to finish the (easy) part. :shock:

If you aren't familiar with how to work with "y = mx + b" or how to evaluate trig functions at pi/2, then I'm afraid you would appear to need much more help than we are able here to give. It is unfortunately that you have no book or class with lessons, so you're stuck trying to work backwards from an answer sheet, but I'm afraid there is nothing that we can do about that. Sorry.

Eliz.

 

[karatekid_81]

i understand where to plug the 2sin(theta) in and the dr/dtheta. I mean just lug it in correct, like any other algebra equation. but the whole theta thing messes me up for some reason

 

[karatekid_81]

i meant to put theta=pi/3