# Which of the following coordinate systems is most common? a. rectangular b. polar c. cylindrical d. spherical Question
Alternate coordinate systems Which of the following coordinate systems is most common?
a. rectangular
b. polar
c. cylindrical
d. spherical 2021-02-16
Step 1
The Coordinate systems are used to locate the thing with respect to the known origin.
Step 2
The system can be classified into 3 types.
Rectangular, Cylindrical and Spherical.
Where rectangular coordinate system is the most commonly used type which is also known as the Cartesian coordinate system.
Thus, a. rectangular coordinate system is the most common.

### Relevant Questions Provide notes on how triple integrals defined in cylindrical and spherical coordinates and the reason to prefer one of these coordinate systems to working in rectangular coordinates. How are triple integrals defined in cylindrical and spherical coor-dinates? Why might one prefer working in one of these coordinate systems to working in rectangular coordinates? How are triple integrals defined in cylindrical and spherical coordinates?
Why might one prefer working in one of these coordinate systems to working in rectangular coordinates? To compare and contrast: the rectangular, cylindrical and spherical coordinates systems. Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: $$\displaystyle{\left({8},{\frac{{\pi}}{{{3}}}},{\frac{{\pi}}{{{6}}}}\right)}$$ Change to cylindrical. Solve the given Alternate Coordinate Systems and give a correct answer 10) Convert the equation from Cartesian to polar coordinates solving for PSKr^2:
\frac{x^2}{9} - \frac{y^2}{16} = 25ZSK Let C be a circle, and let P be a point not on the circle. Prove that the maximum and minimum distances from P to a point X on C occur when the line X P goes through the center of C. [Hint: Choose coordinate systems so that C is defined by
$$x2 + y2 = r2$$ and P is a point (a,0)
on the x-axis with a $$\neq \pm r,$$ use calculus to find the maximum and minimum for the square of the distance. Don’t forget to pay attention to endpoints and places where a derivative might not exist.] Given point P(-2, 6, 3) 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. Consider the solid that is bounded below by the cone $$z = \sqrt{3x^{2}+3y^{2}}$$
and above by the sphere $$x^{2} +y^{2} + z^{2} = 16.$$.Set up only the appropriate triple integrals in cylindrical and spherical coordinates needed to find the volume of the solid. Since we will be using various bases and the coordinate systems they define, let's review how we translate between coordinate systems. a. Suppose that we have a basis$$\displaystyle{B}={\left\lbrace{v}_{{1}},{v}_{{2}},\ldots,{v}_{{m}}\right\rbrace}{f}{\quad\text{or}\quad}{R}^{{m}}$$. Explain what we mean by the representation {x}g of a vector x in the coordinate system defined by B. b. If we are given the representation $$\displaystyle{\left\lbrace{x}\right\rbrace}_{{B}},$$ how can we recover the vector x? c. If we are given the vector x, how can we find $$\displaystyle{\left\lbrace{x}\right\rbrace}_{{B}}$$? d. Suppose that BE is a basis for R^2. If {x}_B = \begin{bmatrix}1 \\ -2 \end{bmatrix}ZSK find the vector x. e. If $$\displaystyle{x}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}\backslash-{4}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{f}\in{d}{\left\lbrace{x}\right\rbrace}_{{B}}$$