x=r cos `theta` y=r sin `theta` `x^(2)` +`y^(2)` =`r^(2)` use above data to rewrite the expressions in trignomtric form y=2 y=`1/4x^(2)` y= -2x+3 `(x-2)^(2)` +`y^(2)` =4    

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embizze | High School Teacher | (Level 1) Educator Emeritus

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(1) Convert y=2 into polar form:

`sintheta=y/r ==> y=rsintheta`

So `rsintheta=2 ==> r=2/sintheta` or `r=2csctheta`

(2) Convert `y=1/4x^2` into polar form:

`x=rcostheta, y=rsintheta` so

`rsintheta=1/4(rcostheta)^2`

`rsintheta=1/4 r^2 cos^2theta`

`4sintheta=rcos^2theta`

`r=(4sintheta)/(cos^2theta)` or `r=4tanthetasectheta`

(3) Convert y=-2x+3 into polar form:

`rsintheta=-2rcostheta+3`

`2rcostheta+rsintheta=3`

`r(2costheta+sintheta)=3`

`r=3/(2costheta+sintheta)`

(4) Convert `(x-2)^2+y^2=4` into polar form:

`x^2-4x+4+y^2=4`

`x^2+y^2-4x=0`   but `x^2+y^2=r^2` so:

`r^2-4rcostheta)=0`

`r^2=4rcostheta`

`r=4costheta`

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