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Express the polar equation r=2costheta i...

Express the polar equation `r=2costheta` in rectangular coordinates.

Text Solution

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We use the formulas `r^2=x^2+y^2` and `x=rcostheta`. ltbr Given `r=2costheta`. Therefore,
`r^2=2rcostheta`
or `x^2+y^2=2x`
or `x^2x+y^2=0`
or `x^2-2x+1+y^2=1`
or `(x-1)^2+y^2=1`.
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Knowledge Check

  • Express sintheta in terms of costheta

    A
    `1/(costheta)`
    B
    `sqrt(costheta)`
    C
    `1-cos theta`
    D
    `+=sqrt(1-cos^2theta)`

  • The polar coordinates of a point P are (2,200^(@)) The rectangular coordinates of P are

    A
    `(-1.88,-0.68)`
    B
    `(-0.68,-1.88)`
    C
    `(-0.34,-0.94)`
    D
    `(-0.47,-0.17)`

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    Express point P whose rectangular coordinates are (3,3sqrt(3)) in terms of polar coordinates r^(2)=x^(2)+y^(2)=9+27=36 r=6 r cos theta =x cos theta =3/6 =1/2 Therefore theta =60^(@) and (6,60^(@)) are the polar coordinates of P

    Find the polar coordinates of the points whose cartesian coordinates are (-2, -2)

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