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

jernplate8 2021-09-04 Answered
Convert the following coordinates between rectangular and polar form
\(\displaystyle{\left({4},-\frac{\pi}{{4}}\right)}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

wornoutwomanC
Answered 2021-09-05 Author has 18691 answers

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

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

Not exactly what you’re looking for?
Ask My Question
2
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...