Question 1157772


a) 

{{{r^2= 7}}}

using the formulae that link Polar to Cartesian coordinates:

{{{r^2=x^2+y^2}}}

{{{x^2+y^2=7}}}-> rectangular form


b) 

{{{theta= 4pi/3}}}

Take the tangent of both sides:

{{{tan(theta)= tan(4pi/3)}}}


Substitute {{{tan(theta)=y/x}}}

{{{y/x= tan(4pi/3)}}}

Multiply both sides by {{{x}}}:

{{{y= tan(4pi/3)*x}}}


Substitute {{{tan(4pi/3)=sqrt(3)}}}


{{{y=sqrt(3)*x}}}-> rectangular form



c) 

{{{theta = 7pi/4}}}

{{{tan(theta) = tan(7pi/4)}}}

{{{y/x= tan(7pi/4)}}}

{{{y/x= -1}}}

{{{y= -x}}}-> rectangular form


d) 

{{{r = cos(theta)}}}

using the formulae that link Polar to Cartesian coordinates:

{{{r^2=x^2+y^2}}}

{{{x=r*cos(theta) }}}and {{{y=r*sin(theta)}}}

for this question given  : {{{r=cos(theta)}}} => {{{r=x/r}}}

multiply both sides by {{{r}}}:  => {{{r*r=xr/r}}} => {{{r^2=x}}}

=> {{{x^2+y^2=x}}}-> rectangular form