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Convert from rectangular form to polar form. 

 

a) (-4,4)

 

b) x^2+(y-5)^2=25

 May 12, 2020
 #1
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a)  (-4, 4)

 

r =  sqrt [ (-4)^2 + 4^2]  =  sqrt [32]  =  4sqrt (2)

 

θ  =  arctan (4/-4)  = arctan (-1)  =  -pi/ 4     ....this is a point in te second quadrant  so θ = -pi/4 + pi =

3pi/4

 

So   (r, θ)  =  ( 4sqrt 2, 3pi/4)

 

 

(b)  x^2 + (y - 5)^2   = 25      expand

 

x^2  + y^2 - 10y + 25 =  25      subtract 25 from both sides

 

x^2  + y^2  - 10y   =  0

 

r^2cos^2θ + r^2sin^2θ - 10 ( r sinθ)  = 0

 

r^2 ( cos^2θ + sin^2θ)  =  10r (sin θ)

 

r^2 (1)  = 10r (sin θ)        divide out r

 

r  = 10sinθ

 

 

cool cool cool

 May 12, 2020

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