Question

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

Answer 1

`(-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))" ")|)`

Answer 2

`(-(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)`