Polar Curves Flashcards
How to plot polar curves
Put the equation in the table thing based on steps of pi /2
- so this means that if it’s 2theta m then make it pi /4
Now when it’s above 0 itsstraight snd be,ow it’s negative
- here the fire too into you have, plot it there, doesn’t have to start from 0
- then plot the secon point. If it’s going to 0 imagine how it increase and decfeease for bales and how it will look like
Normally circular motion, and will be even d
Converting from polar to Cartesian
Either sqaure both sides or mutlipy by r, or by cos as this will give you oprptoutnit ti cinver
Thing is in Cartesian yiu lose the negative dotted growth bit because sqaure root function id alwyaspositb. ,
What happens for limacons a +b cos or sin theta with diff vslues for a and b ?
If a less than b, then it goes inside
If a = b = carodiod, so cusp heart
A >b = if it is grsdient
Sin reflected centred y axis same thing
Amd for limacons if itd 1 - cos theta etc what to do
It’s the same concept a bigger than b etc, just REFLECTED
so I’m this case this is carotid REFLECTED
What about cos (2x)
Sin?
Odd values?
Thid gives you petal thing , where number of petals = 2 times the bracket
Might be covered by negative dont lack
Sin same thing centred on y acis
Odd values will be the stuck ones
R = k theta?
This is spiral of Archimedes, r takes a Stil value of theta, so pi/2 so 1.5, then 3.14 then again and again so each time it gets bigger
R = psec (a-theta)
This is a straight line, where p is the distance from Irgun, and alpha is the angle that tms gent makes
Then just sub in vslues for where it crossed to get interceptions
Alternsotvly make a straight line out of it first heimgekommen Cartesian compund etc
To find the
Olaf curve equation
Use trig values, remember dismeter is the hypotenuse
Or make Cartesian first and try manipulate it back
How find area
Would be the sum of all sectors as we using theta, so sector area = 1/2 r2 theta
So 1/2 (integral between angles enclosing space of r2)
How might convert sin2 cuz you can’t integrate that normally
Use cos2theta trig thing and manipulate Remmeber the multipy by 2
Remmeber the negative area counts and you can integrate whole thing and divide etc
What about gradient
Must convert to caerteisanm IMplicit then leave as it is
Find x and y by subbing in theta to find r (use the positive grsdient ) and sub thes in rerasnrge rtv
If it says find area when r is more than 0
Ignore negative regions, remember to remember this.!
Area between two curves
Draw them
Find the intersections
Identity which parts of areas are in what graph
Integrate to that
Do it sgsin
End
To equate ,ignt have to convert into harmonic form too
How to find tangents parallel perpendicular
Find dy / d theta for parallel and dx for units,
Set to 0
Find the angle , look at graph tonsee how many should be
Now find r , try make it exact
Now sub in ti y = rsi. Theta etc
With symmetry these should be similar
Chekc angle for subbing back into the equation
You need ti find r , then sub unit x =
Or just sub into x = thing straight awya, especially if angles are just linear
