Question 1121000
<pre>
Solve the system: {{{system(r*sin(theta)=3, r=4(1+sin(theta)^""))}}}

Substitute the value of r from the second equation in the first equation:

{{{r*sin(theta)=3}}}

{{{4(1+sin(theta)^"")*sin(theta)=3}}}

{{{4*sin(theta)*(1+sin(theta)^"")=3}}}

{{{4*sin^""(theta)+4sin^2(theta)^""=3}}}

{{{4*sin^""(theta)+4sin^2(theta)^""-3=0}}}

Swap the first two terms:

{{{4sin^2(theta)^""+4*sin^""(theta)-3=0}}}

Factor the left side:

{{{(2sin(theta)+3^"")(2sin(theta)-1^"")=0}}}

{{{2sin(theta)+3=0}}},   {{{2sin(theta)-1=0}}}
{{{2sin(theta)=-3}}},   {{{2sin(theta)=1}}}  
{{{cross(sin(theta)=-3/2)}}},   {{{sin(theta)=1/2}}}

All sines are between -1 and +1 so -3/2 is not a possibility,
so we ignore the left equation.

{{{sin(theta)=1/2}}}

{{{theta=matrix(1,3,30^o+360^o*n,or,150^o+360^o*n)}}}, if &theta; is in degrees. 

or

{{{theta=matrix(1,3,pi/6+2pi*n,or,5pi/6+2pi*n)}}}, if &theta; is in radians. 

Substituting in the first given equation:

{{{r*sin(theta)=3}}}
{{{r*(1/2)=3}}}
{{{expr(1/2)r=3}}}
{{{r=6}}}

Edwin</pre>