How do you convert #[3, -5pi/4]# into rectangular coordinates?

2 Answers
Aug 6, 2017

Answer:

#(-2.121, 2.121)#

Explanation:

We're asked to find the rectangular coordinate of a given polar coordinate.

In order to do this, we use the equations

#ul(x = rcostheta#

#ul(y = rsintheta#

where in this case

  • #r = 3#

  • #theta = (-5pi)/4#

Thus, we have

#x = 3cos((-5pi)/4) = color(red)(ul(-2.121#

#y = 3sin((-5pi)/4) = color(green)(ul(2.121#

The coordinate is therefore

#ulbar(|stackrel(" ")(" "(color(red)(-2.121), color(green)(2.121))" ")|)#

Aug 6, 2017

Answer:

#(-(3sqrt2)/2,(3sqrt2)/2)#

Explanation:

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

#"that is "(r,theta)to(x,y)" using"#

#•color(white)(x)x=rcostheta" and " y=rsintheta"#

#"here " r=3" and "theta=-(5pi)/4#

#rArrx=3xxcos(-(5pi)/4)#

#color(white)(rArrx)=-3xxcos(pi/4)#

#color(white)(rArrx)=-3xx1/sqrt2=-(3sqrt2)/2#

#rArry=3xxsin(-(5pi)/4)#

#color(white)(rArry)=3xxsin(pi/4)#

#color(white)(rArry)=3xx1/sqrt2=(3sqrt2)/2#

#rArr(3,-(5pi)/4)to(-(3sqrt2)/2,(3sqrt2)/2)#