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polar curves

slopes arc-lengths and areas of polar curves

tanw = f(thetha) /f`(thetha)

area bounded by part of polar curve drawn.maybe a 4-leaf rose , find the value of thetha for which one leaf start ... till its thetha at end point. use that as your integration factors , use the formula area = 0.5r^2d thetha , and then multiply with number of leaf , in this case 4. Understand when we were integrating , we solved the area of one leaf only.

arc-lenghs of polar curves

s= Root f(thetha)prime squared + f(thetha)squared.

(Polar cordinates

*polar co-ordinates are not unique like cartesian co-ordinates.eg. (r , thetha ) =(r , thetha+2kpie) where k = +-1 , +-2, +-3 ...etc

x=rcos(thetha)

y=rsin(thetha)

x^2 +y^2 =r^2

y/x=tan(thetha

sketching of polar graphs

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