Question 983183

The rectangular coordinates ({{{x}}} , {{{y}}}) and polar coordinates ({{{R}}} ,{{{ theta}}}) are related as follows.

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

{{{R^2 = x^2 + y^2}}}    and    {{{tan (theta) = y / x}}}


so,

if  polar coordinates ({{{R}}} , {{{theta}}}) are ({{{-2}}} , {{{-36}}}) , then we have

{{{y = -2*sin( 36 )}}}   and    {{{x = -2cos( 36)}}}

{{{y = -2 (sqrt((5/8) - sqrt(5)/8))}}}   and   {{{ x = -2((1/4)(1+sqrt(5)))}}}

exact result:

{{{y = -2 (sqrt((5/8) - sqrt(5)/8))}}}   and   {{{ x = - ((1/2) (1+sqrt(5)))}}}

approximate:

{{{y = -1.18}}}  and   {{{ x = -1.62}}}

so, the rectangular coordinates of the point ({{{x}}} , {{{y}}}) are ({{{1.62}}},{{{-1.18}}})