How do you find the rectangular coordinates given the polar coordinates #(1/2, (3pi)/4)#?

1 Answer
Jim G.
Dec 8, 2016

#(-sqrt2/4,sqrt2/4)#

Explanation:

To convert from #color(blue)"polar to rectangular coordinates"#

That is #(r,theta)to(x,y)#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(x=rcostheta , y= rsintheta)color(white)(2/2)|)))#

#"Here " r=1/2" and " theta=(3pi)/4#

#rArrx=1/2cos((3pi)/4)" and " y=1/2sin((3pi)/4)#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(cos((3pi)/4)=-cos(pi/4)=-1/sqrt2)color(white)(2/2)|)))#

and #color(red)(bar(ul(|color(white)(2/2)color(black)(sin((3pi)/4)=sin(pi/4)=1/sqrt2)color(white)(2/2)|)))#

#rArrx=1/2cos(pi/4)=1/2xx-1/sqrt2=-1/(2sqrt2)=-sqrt2/4#

and #y=1/2sin(pi/4)=1/2xx1/sqrt2=sqrt2/4#

#rArr(1/2,(3pi)/4)to(-sqrt2/4,sqrt2/4)#

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