Unformatted text preview: the circle, so canceling r does not eliminate r = 0 as a potential solution of the equation (since θ = ◦ would make r = 8 sin θ = 8 sin 0 ◦ = 0). Thus, the equation is r = 8 sin θ . Example 6.19 Write the equation y = x in polar coordinates. Solution: This is the equation of a line through the origin. So when x = 0, we know that y = 0. When x n= 0, we get: y = x y x = 1 tan θ = 1 θ = 45 ◦ Since there is no restriction on r , we could have r = 0 and θ = 45 ◦ , which would take care of the case x = 0 (since then ( x , y ) = (0,0), which is the same as ( r , θ ) = (0,45 ◦ )). Thus, the equation is θ = 45 ◦ ....
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 Fall '11
 Dr.Cheun
 Calculus, Addition, potential solution, Coordinate system, Polar coordinate system

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