- #1
bobsmith76
- 336
- 0
Homework Statement
Homework Equations
The Attempt at a Solution
Do you see that 2 between A and the integral? There's no 2 in the above equation. I don't see where that 2 came from. Everything else is fine.
Converting polar to cartesian coordinates
- Thread starter bobsmith76
- Start date
In summary, the formula for converting polar coordinates to cartesian coordinates is x = r * cos(θ) and y = r * sin(θ). To plot a point in cartesian coordinates, convert the polar coordinates using this formula and then plot the point. Some advantages of using polar coordinates include their ability to represent curved shapes and their usefulness in physics and engineering problems. Negative values can be represented in polar coordinates and to convert cartesian coordinates to polar coordinates, use the formulas r = √(x^2 + y^2) and θ = tan⁻¹(y/x).
Do you see that 2 between A and the integral? There's no 2 in the above equation. I don't see where that 2 came from. Everything else is fine.
- #2
Ninty64
- 46
- 0
The 2 comes from the symmetry. 0 to pi/4 on the sine circle is only calculating the bottom-right half of the area.
- #3
jaqueh
- 57
- 0
because if you just did it with no 2*the integral then you would only get the area of half of your region
Related to Converting polar to cartesian coordinates
1. What is the formula for converting polar coordinates to cartesian coordinates?
The formula for converting polar coordinates (r, θ) to cartesian coordinates (x, y) is:
x = r * cos(θ)
y = r * sin(θ)
2. How do you plot a point in cartesian coordinates if given its polar coordinates?
To plot a point in cartesian coordinates, first convert the polar coordinates (r, θ) to cartesian coordinates (x, y) using the formula:
x = r * cos(θ)
y = r * sin(θ)
Then, plot the point (x, y) on the cartesian plane.
3. What are the advantages of using polar coordinates over cartesian coordinates?
One advantage of using polar coordinates is that they can represent curved and circular shapes more easily than cartesian coordinates. Additionally, polar coordinates are often used in physics and engineering problems involving forces and motion, as they can simplify calculations and equations.
4. Can negative values be represented in polar coordinates?
Yes, negative values can be represented in polar coordinates. The distance from the origin, r, can be negative if the point is located in the opposite direction from the positive x-axis. The angle θ can also be negative if the point is located in the lower left quadrant of the cartesian plane.
5. How do you convert cartesian coordinates to polar coordinates?
To convert cartesian coordinates (x, y) to polar coordinates (r, θ), use the formulas:
r = √(x^2 + y^2)
θ = tan⁻¹(y/x)
Note: If x is negative, add π to θ. If x is positive and y is negative, add 2π to θ.
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