# Convert the following coordinates between rectangular and polar form(4,-pi/4)

Convert the following coordinates between rectangular and polar form
$$\displaystyle{\left({4},-\frac{\pi}{{4}}\right)}$$

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$$\displaystyle{\left({4},-\frac{\pi}{{4}}\right)}$$
$$\displaystyle\therefore{r}={4},\theta=-\frac{\pi}{{4}}$$
$$\displaystyle\therefore{x}={r}{\cos{\theta}}={4}{\cos{{\left(-\frac{\pi}{{4}}\right)}}}={4}\cdot\frac{\sqrt{{2}}}{{2}}={2}\sqrt{{2}}$$
$$\displaystyle{y}={r}{\sin{\theta}}={4}{\sin{{\left(-\frac{\pi}{{4}}\right)}}}={4}\cdot{\left(-\frac{\sqrt{{2}}}{{2}}\right)}=-{2}\sqrt{{2}}$$

$$\therefore$$The cartesian/rectangle coordinate
$$\displaystyle{\left({x},{y}\right)}={\left({2}\sqrt{{2}},-{2}\sqrt{{2}}\right)}$$