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

##### 2 Answers
Aug 9, 2017

$\left(4 \sqrt{2} , - 4 \sqrt{2}\right)$

#### 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,

• $r = 8$

• $\theta = - {45}^{\text{o}}$

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)" ")|)

Aug 9, 2017

$\left(4 \sqrt{2} , - 4 \sqrt{2}\right)$

#### Explanation:

$\text{to convert from "color(blue)"polar to rectangular coordinates}$

$\text{that is "(r,theta)to(x,y)" using}$

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

$\text{here " r=8" and } \theta = - {45}^{\circ}$

$\Rightarrow x = 8 \cos {\left(- 45\right)}^{\circ} = 8 \cos {\left(45\right)}^{\circ} = 8 \times \frac{1}{\sqrt{2}} = 4 \sqrt{2}$

$y = 8 \sin {\left(- 45\right)}^{\circ} = - 8 \sin {\left(45\right)}^{\circ} = - 8 \times \frac{1}{\sqrt{2}} = - 4 \sqrt{2}$

$\Rightarrow \left(8 , - {45}^{\circ}\right) \to \left(4 \sqrt{2} , - 4 \sqrt{2}\right)$