For the polar point (-4, -\frac{3 \pi}{4})a) Give alternate coordinates

SchachtN 2021-09-29 Answered

For the polar point \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}\)
a) Give alternate coordinates with \(\displaystyle{r}{>}{0}\) and \(\displaystyle-{2}\pi\leq\theta{<}{0}\).
b) Give alternate coordinates with \(\displaystyle{r}{<}{0}\) and \(\displaystyle{0}\leq\theta{<}{2}\pi\).
c) Give alternate coordinates of your choice.

Expert Community at Your Service

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

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Willie
Answered 2021-09-30 Author has 17796 answers
Step 1
Given: \(\displaystyle{P}{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}\)
a) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},-{\frac{{{3}\pi}}{{{4}}}}+\pi\right)}\)
\(\displaystyle={\left({4},{\frac{{\pi}}{{{4}}}}\right)}\)
So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},{\frac{{\pi}}{{{4}}}}\right)}\)
Step 2
b) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}+{2}\pi\right)}\)
\(\displaystyle={\left(-{4},-{\frac{{{5}\pi}}{{{4}}}}\right)}\)
So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left(-{4},{\frac{{{5}\pi}}{{{4}}}}\right)}\)
c) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},-{\frac{{{3}\pi}}{{{4}}}}+{3}\pi\right)}\)
\(\displaystyle={\left({4},{\frac{{{9}\pi}}{{{4}}}}\right)}\)
So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},{\frac{{{9}\pi}}{{{4}}}}\right)}\)
Have a similar question?
Ask An Expert
21
 
content_user
Answered 2021-10-29 Author has 2505 answers

Answer is given below (on video)

0

Expert Community at Your Service

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

Relevant Questions

asked 2021-08-01

For the polar point \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}\)
a) Give alternate coordinates with \(\displaystyle{r}{>}{0}\) and \(\displaystyle-{2}\pi\leq\theta{<}{0}\).
b) Give alternate coordinates with \(\displaystyle{r}{<}{0}\) and \(\displaystyle{0}\leq\theta{<}{2}\pi\).
c) Give alternate coordinates of your choice.

asked 2021-06-05
The Cartesian coordinates of a point are given.
a) \((2,-2)\)
b) \((-1,\sqrt{3})\)
Find the polar coordinates \((r,\theta)\) of the point, where r is greater than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)
Find the polar coordinates \((r,\theta)\) of the point, where r is less than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)
asked 2021-01-02

Solve the given Alternate Coordinate Systems and give a correct answer 10) Convert the equation from Cartesian to polar coordinates solving for \(r^2\):
\(\frac{x^2}{9} - \frac{y^2}{16} = 25\)

asked 2021-08-05
We can describe the location of a point in the plane using different ________ systems. The point P shown in the figure has rectangular coordinates ( _ , _ ) and polar coordinates ( _, _).
asked 2021-01-23

Give a correct answer for given question

(A) Argue why \({ (1,0,3), (2,3,1), (0,0,1) }\) is a coordinate system ( bases ) for \(R^3\) ?

(B) Find the coordinates of \((7, 6, 16)\) relative to the set in part (A)

asked 2021-09-21
The Cartesian coordinates of a point are given.
a) \(\displaystyle{\left({2},-{2}\right)}\)
b) \(\displaystyle{\left(-{1},\sqrt{{{3}}}\right)}\)
Find the polar coordinates \(\displaystyle{\left({r},\theta\right)}\) of the point, where r is greater than 0 and 0 is less than or equal to \(\displaystyle\theta\), which is less than \(\displaystyle{2}\pi\)
Find the polar coordinates \(\displaystyle{\left({r},\theta\right)}\) of the point, where r is less than 0 and 0 is less than or equal to \(\displaystyle\theta\), which is less than \(\displaystyle{2}\pi\)
asked 2021-08-02
Given point \(\displaystyle{P}{\left(-{2},{6},{3}\right)}\) and vector \(\displaystyle{B}={y}{a}_{{{x}}}+{\left({x}+{z}\right)}{a}_{{{y}}}\), Express P and B in cylindrical and spherical coordinates. Evaluate A at P in the Cartesian, cylindrical and spherical systems.
...