Textbook Question
Cartesian to Polar Coordinates
Find the polar coordinates, 0 ≤ θ ≤ 2π and r ≤ 0, of the following points given in Cartesian coordinates.
c. (−1, √3)
1
views
Ch. 11 - Parametric Equations and Polar Coordinates
Hass15th EditionThomas' CalculusISBN: 9780137616077
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions489
- Ch. 8 - Techniques of Integration398
- Ch. 9 - First-Order Differential Equations60
- Ch. 10 - Infinite Sequences and Series119
- Ch. 11 - Parametric Equations and Polar Coordinates58
Chapter 11, Problem 11.3.6c
Polar to Cartesian Coordinates
Find the Cartesian coordinates of the following points, given in polar coordinates.
c. (0, π/2)
Verified step by step guidance1
Recall the formulas to convert from polar coordinates \((r, \theta)\) to Cartesian coordinates \((x, y)\):
\[x = r \cdot \cos(\theta)\]
\[y = r \cdot \sin(\theta)\]
Substitute the given polar coordinates \((r, \theta) = (0, \frac{\pi}{2})\) into the formulas:
Calculate the values of \(x\) and \(y\) using the substituted values without simplifying the final numeric result.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polar Coordinates
Polar coordinates represent a point in the plane using a radius and an angle, denoted as (r, θ). The radius r is the distance from the origin, and θ is the angle measured from the positive x-axis, usually in radians.
Recommended video:
05:32
Intro to Polar Coordinates
Conversion Formulas from Polar to Cartesian
To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the formulas x = r * cos(θ) and y = r * sin(θ). These relate the radius and angle to horizontal and vertical distances.
Recommended video:
3:37Convert Equations from Rectangular to Polar
Special Case: Zero Radius
When the radius r is zero, the point is at the origin regardless of the angle θ. This means the Cartesian coordinates are always (0, 0) for any angle if r = 0.
Recommended video:
04:24Graphing The Derivative - Special Cases
Related Practice
Textbook Question
Theory and Examples
Volume Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x² + 4y² = 36 about the y−axis.
1
views
Textbook Question
Cartesian to Polar Coordinates
Find the polar coordinates, 0 ≤ θ < 2π and r ≥ 0, of the following points given in Cartesian coordinates.
b. (-3,0)
1
views