Question 1157770

a) ({{{1}}},{{{0}}})

{{{r=sqrt(x^2+y^2)}}}
{{{r=sqrt(1^2+0^2)}}}
{{{r=1}}}

{{{theta =tan^-1 (y/x)}}}
{{{theta =tan^-1 (0/1)}}}
{{{theta =tan^-1 (0)}}}
{{{theta =0}}}radians


=>the polar coordinates: ({{{1}}},{{{0}}})

b) ({{{0}}},{{{-4}}})

{{{r=sqrt(x^2+y^2)}}}
{{{r=sqrt(0^2+(-4)^2)}}}
{{{r=sqrt(16)}}}
{{{r=4}}}

{{{theta =tan^-1(y/x)}}}

{{{theta =tan^-1(-4/0)}}}-> undefined

the polar coordinates of ({{{0}}},{{{ -4}}} ) is ({{{4}}}, {{{undefined }}})


c) ({{{3}}},{{{-3}}})

{{{r=sqrt(x^2+y^2)}}}
{{{r=sqrt(3^2+(-3)^2)}}}
{{{r=sqrt(9+9)}}}
{{{r=sqrt(2*9)}}}
{{{r=3sqrt(2)}}}

{{{theta =tan^-1 (y/x)}}}
{{{theta =tan^-1 (-3/3)}}}
{{{theta =tan^-1 (-1)}}}
{{{theta =-pi/4}}}

the polar coordinates: ({{{3sqrt(2)}}}, {{{-pi/4}}})


d) ({{{-1}}},{{{2}}})

{{{r=sqrt(x^2+y^2)}}}
{{{r=sqrt((-1)^2+2^2)}}}
{{{r=sqrt(1+4)}}}
{{{r=sqrt(5)}}}

{{{theta =tan^-1 (y/x)}}}
{{{theta =tan^-1 (2/-1)}}}
{{{theta =tan^-1 (-2)}}}
{{{theta =-1.107}}}

the polar coordinates:  ({{{sqrt(5)}}},{{{-1.107}}})