Question

How can `(8,-45º)` be converted into rectangular coordinates?

Answer 1

`(4sqrt2, -4sqrt2)`

Explanation:

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

To do this, we use the equations

`ul(x = rcostheta`

`ul(y = rsintheta`

In this case,

• `r = 8`

• `theta = -45^"o"`

So we have

`x = 8cos(-45^"o") = ul(4sqrt2`

`y = 8sin(-45^"o") = ul(-4sqrt2`

The coordinate is thus

`color(blue)(ulbar(|stackrel(" ")(" "(4sqrt2, -4sqrt2)" ")|)`

Answer 2

`(4sqrt2,-4sqrt2)`

Explanation:

`"to convert from "color(blue)"polar to rectangular coordinates"`

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

`•color(white)(x)x=rcosthetacolor(white)(x);y=rsintheta"`

`"here " r=8" and "theta=-45^@`

`rArrx=8cos(-45)^@=8cos(45)^@=8xx1/sqrt2=4sqrt2`

`y=8sin(-45)^@=-8sin(45)^@=-8xx1/sqrt2=-4sqrt2`

`rArr(8,-45^@)to(4sqrt2,-4sqrt2)`