FM: Pure: Polar Coordinates

what are the form of polar coordinated

(r,θ)

what are angles usually measured in when using polar coordinates

angles are normally measured in radians when using polar coordinates . If the angle can be expressed as a multiple of , as for point C in Example 1, then always do so unless you are instructed otherwise.

what is the (x,y) system of coordinates referred to as

cartesian system

to find the gradient of the polar curve what must you do

convert to cartesian form before differentiating

what does differentiating the polar curve do

gives you the rate of change of r with respect to θ which is not the same as the gradient of a polar curve

what do polar coordinates have

polar coordinates give an alternative method of describing the location of a point in the two-dimensional plane

what does r stand for

the distance of the point P from the origin

how do you know exactly what the θ is in the polar coordinates

the equation tanθ=y/x always gives two solutions in the range -π<θ≤π you must select the correct one by considering in which quadrant the point lies

what does θ stand for

usually measured in degrees or radians in an anticlockwise direction from the intial line which is drawn horizontally to the right

for converting polar coordinates to cartesian coordinates what formulae must you follow

x=rcosθ y=rsinθ