# Math

Let the polar coordinates of the point (x, y) be (r, θ). Determine the polar coordinates for the point (2x, y)

1. 👍 0
2. 👎 0
3. 👁 133
1. For (x,y), we have
r^2 = x^2 + y^2
tanθ = y/x
Let the new point have polar coordinates (p,φ). Then
p^2 = (2x)^2 + y^2 = 4x^2 + y^2 = r^2 + 3x^2
tanφ = y/(2x) = 1/2 (y/x) = 1/2 tanθ

You can massage those into other forms, of course.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### calc 3

Use polar coordinates to find the limit. [If (r, θ) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.) lim (x, y)→(0, 0) [(3e^−x^2−

asked by Becky on September 17, 2012
2. ### math

Determine two pairs of polar coordinates for (3,-3) when 0°

asked by Lilly on July 22, 2013
3. ### Math

The letters r and θ represent polar coordinates. Write the following equation using rectangular coordinates (x, y). Given equation r=5

asked by Jolyne Kujo on March 20, 2019
4. ### CHEMISTRY

Determine if it is polar or non-polar molecule: C3H6O C2H5OH SiCl4 NH3 CO2 C3H8 H2O N2 My ans are: Polar Polar Polar Nonpolar polar Nonpolar are my answers correct????

asked by nidscorection on March 5, 2013
5. ### pre-calc help

Convert the rectangular coordinates to polar coordinates with r > 0 and 0 ≤ θ < 2π. (9, −9) (r, θ) = ?

asked by Anonymous on November 27, 2013
1. ### Calc

Find the cartesian coordinates of the following points given in polar coordinates. b. (2 rt2, 3pi/4) I cant figure this one out

asked by Jessica on March 26, 2008
2. ### Physics

Two points in the xy plane have Cartesian coordinates (2.00, -4.00) m and (-5.00, 5.00) m. (a)What is the distance between these two points? (b) What are their polar coordinates?

asked by Vivian on January 13, 2010
3. ### Trig (math)

1.) Find all solutions of the equation. Leave answers in trigonometric form. x^2 + 1 - sqrt3i = 0 2.) Give the rectangular coordinates for the point. (9, 2pi/3) 3.) The rectangular coordinates of a point are given. Express the

asked by Anonymous on December 8, 2014
4. ### Precalculus

Every point in the plane has exactly two polar coordinates. A)The statement is true because every point in the plane has a unique polar representation. B)The statement is false because left parenthesis r comma theta right

asked by Brian on January 12, 2017
5. ### trig

convert the point with polar coordinates (2,7pi/6) into rectangular coordinates.

asked by casey on April 19, 2011