# cartesian

1. ### Cartesian -> Spherical polar

I have an integral \int \int_S x^2 + yz \ dS and wish to transform to spherical polar coordinates. How does dS become dS = r^2 \sin \theta d\theta d\phi ?? Where surface S is x^2 + y^2 + z^2 = 1
2. ### Cartesian equation.

Would someone mind telling me how to find the indicated direction in the problem below? Help with (b) would also be greatly appreciated! (a) Graph the parametrized curve described by x = 2 cos t, y = -sin t, 0≤t≤pi. Indicate the direction in which the curve is traced. (b) Find a Cartesian...
3. ### circle in the cartesian plane question. (coordinate geometry)

Find the equation of the circle which is tangential to the axis (2,0) and touches the line y=6 Unsure of workings? Answers are; A, (x+2)^2 + (y-7)^2 = 26 B, 2x -y = 5 C, k = 0 Cheers Neils=)
4. ### Cartesian equations

Given x=2 \sin (nt+\frac{\pi}{3}) and y=4 \sin (nt+ \frac{\pi}{6}), express x and y in terms of \sin nt and \cos nt. Find the Cartesian equation of the locus of the point (x,y) as t varies. I have expressed x and y in terms of \sin nt and \cos nt already. x=2 \sin (nt+\frac{\pi}{3})...
5. ### Cartesian Coordinates of Planets in Orbit Relative to Time

Hello everyone, I've been searching for days to find a simple method of calculating the X,Y,Z coordinates of a planet that is in orbit at any point in time around another planet/star/sun. All of the related resources I've found are heavily focused on finding values based on observing actual...
6. ### Cartesian eqn of a plane

A plane passes through the P, with position vector i + 2j - k, and is perpendicular to the line L with eqn r = 3i -2k + w(-i + 2j + 3k) Show that the Cartesian eqn of the plane is x - 5y -3z = -6 I'm not sure how to work out the normal of the plane?
7. ### Cartesian Product

Hi! I'm trying to self-study some math and I've decided to "forget" almost but high school math and start from the beggining. I have a seriously easy question about Cartesian Product. It is true that (\mathbb{R}^{2} \times \mathbb{R}=\mathbb{R} \times \mathbb{R}^{2}=\mathbb{R}^3) ? I've...
8. ### Question related to cartesian vectors

Find two perpendicular vectors such that one of these vectors is twice as long as the other, and their sum is the vector [6,8]. I tried the following approach. Let's say that u = [u1,u2] and v=[v1,v2]. Then we would have the u1v1 = -u2v2. I also got the following equations. u1+v1=6 u2+v2=8...
9. ### Three dimensional cartesian plane

This might not be the right forum for the question, please forgive. I know it doesn't matter which way we look at the xyz cube its all the same, but why does my text make the z axis the vertical axsis instead of the y. I have been used to looking at xy plane all my life and it throws me off. I...
10. ### conversion from cartesian to parametric form

hi all, given the implicit equation x^2+x+1-y^2 = 0, how can i find the parametric form of this equation, i.e.: x = f(t) y = f(t) thanks in advance for the help.
11. ### Cartesian equation for a curve

Hey guys i need help with this question for an assignment. Find a Cartesian equation for the curve and identify it: r = 2sin(θ) + 2cos(θ) i tried multipliying everything by r, getting: r^2 = 2rsin(θ) + 2rcos(θ) then making r^2 = x^2 + y^2 and making...
12. ### Equivalence Classes for a Cartesian Plane Relation

Greetings, If a relation is defined on the Cartesian plane \mathbb{R} \times \mathbb{R} by (x_1,y_1) \; \backsim \; (x_2,y_2) \; \Longleftrightarrow \; (x_2,y_2) \; = \; (rx_1,ry_1) for some r \; > \; 0, what would the equivalence classes be? This seems like it should be easy, but I'm drawing a...
13. ### Cartesian Proof Sets

Prove: A × B = ∅ if and only if A = ∅ or B = ∅.
14. ### Cartesian equation of tangent of ellipse

Show that for all values of m, the straight lines with equations y=mx\pm \sqrt(b^2+a^2m^2) are tangents to the ellipse with equation \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 Heelp
15. ### Doing a Cartesian Product/Direct Sum?

Let V = R^2 and W be the subspace generated by w=(2,3). Let U be the subspace generated by u=(1,1). Show that V is the direct sum of W and U. Can you generalize this to any two vectors u and w? My attempt to generalize: V=W+U =r(w1 w2) + s(u1 u2) =(rw1 rw2) + (su1 su2) =(rw1+su1...
16. ### Some Cartesian product questions

Hello guys, A question goes as follows: "Let S be the set of all sequences \{a_n\}_n satisfying |a_1|<1, |a_3|<2, |a_4|<1. Express S as a cartesian product of subsets of the real numbers" I know in this instance that a_1 \in [-1,1], a_3 \in [-2,2], a_4 \in [-1,1]. But I'm confused as to how to...
17. ### Calc Cartesian Equation

A curve is parametrized by x=t, y=the square root of (t+2), t is greater than or equal to -2. Write a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?
18. ### Cartesian products of Sets

For A={ the empty set , {the empty set}}. Determine A X P(A)
19. ### converting parametric equations into cartesian form

show that x = sin t and y = sin (t + pi/6) can be written in the form y = ax + b√1-x^2 stating the values of a and b im really stuck
20. ### Prove a countable Cartesian product of countable sets is uncountable

Hey guys, could you please check over my solution and let me know if I made a mistake somewhere? Problem: Let A_1, A_2, A_3, ... be countable sets. Then show that the Cartesian product A = A_1 \times A_2 \times A_3 \times ... is uncountable. In other words, show that the set of countably...