Given, \((x, y) = (4, −4)\) For the polar coordinates \(r = \sqrt{x^2 + y^2}\ and\ \theta = tan^−1 (\frac{y}{x})\)
\(r = \sqrt{16 + 16}\)
\(r = \sqrt{32}\)
\(r = 4 \sqrt 2\) And \(\theta = tan^-1 (\frac{-4}{4}\)
\(\theta = tan^-1 (-1)\)
\(\theta = \frac{\pi}{4}\) The two sets of polar coordinates are \((-4 \sqrt2, \frac{\pi}{4}). (4 \sqrt2, \frac{\pi}{4})\)
Question
The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for 0 < 2.
Answers (1)
2021-02-05
Relevant Questions
asked 2021-06-09
Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)
a) \((-2, 2, 2)\)
b) \((-9,9\sqrt{3,6})\)
c) Use cylindrical coordinates.
Evaluate
\(\int\int\int_{E}xdV\)
where E is enclosed by the planes \(z=0\) and
\(z=x+y+10\)
and by the cylinders
\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)
d) Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
\(z=\sqrt{x^{2}+y^{2}}\)
and the sphere
\(x^{2}+y^{2}+z^{2}=8\).
a) \((-2, 2, 2)\)
b) \((-9,9\sqrt{3,6})\)
c) Use cylindrical coordinates.
Evaluate
\(\int\int\int_{E}xdV\)
where E is enclosed by the planes \(z=0\) and
\(z=x+y+10\)
and by the cylinders
\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)
d) Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
\(z=\sqrt{x^{2}+y^{2}}\)
and the sphere
\(x^{2}+y^{2}+z^{2}=8\).
asked 2021-06-08
1) Find the area of the part of the plane
4x + 3y + z = 12
that lies in the first octant.
2) Use polar coordinates to find the volume of the given solid.
Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant
4x + 3y + z = 12
that lies in the first octant.
2) Use polar coordinates to find the volume of the given solid.
Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant
asked 2021-05-08
Find the points on the cone \(z^2 =x^2+y^2\) that are closest tothe point (2, 2,0).
asked 2021-06-11
Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).
