Polar form and Cartesian form

Question	Answer
What is the notation for a polar coordinate?	(r,θ)
What equations do we use to convert from Polar form to Cartesian form?	x = rcosθ y = rsinθ
What equations do we use to convert from Cartesian form to Polar form?	r = root(x^2 + y^2) tanθ = y/x
Convert (3,4) into polar form	root(3^2 + 4^2) = 5 tanθ = 4/3 , tan-1(4/3) = 0.927 (5,0.927)
The origin is also called....	The pole (the point where the r value is measured from)
The x-axis is also called....	The initial line (where the angle θ is measured AC from)
On a polar graph, 5/4π is also equal to....	-3/4π (CW) , 13/4π (AC + 2π) , π/4 (AC if r is flipped to be negative)
Remember to +/- π depending on.....	The quadrant of the polar graph (or depending on if the angle is CW or AC)
A(3,π/3) , B(4-3/8π) , Find \|AB\|	Image: Capture (binary/octet-stream)
Write y=x^2 as a polar equation	rsinθ = (rcosθ)^2 rsin = r^2cos^2θ Given that r≠0 , we get the polar equation: sinθ=rcos^2θ
Write (-2,4) in polar form for both r>0 and r<0	r = root(2^2+4^2) = 2(root 5) tanθ = 4/2 , tan-1(2) = 1.11 r>0 ; π-1.11 = 2.04 , so (2(root 5) , 2.04) r<0 ; (-2(root 5) , 1.11)

Resource summary

	Created by Doc Boff almost 7 years ago