# Where Do Polar Curves r=5sin(theta) and r=5cos(theta) Intersect?

• MHB
• joshuapeterson
In summary, polar coordinates are a system used to represent points in a two-dimensional plane using distance and angle. To convert between polar and Cartesian coordinates, specific formulas are used. The intersection of two polar coordinates is the point where the two lines representing them intersect. To find this intersection, the coordinates are converted to Cartesian, equations are set equal to each other, and the resulting values are converted back to polar. This intersection is significant in various scientific fields as it allows for efficient representation and analysis of data involving circular or rotational movement. It is also commonly used in astronomy and navigation.
joshuapeterson
Determine the polar coordinates of the two points at which the polar curves r=5sin(theta) and r=5cos(theta) intersect. Restrict your answers to r >= 0 and 0 <= theta < 2pi.

Aren't you going to at least attempt it yourself? r= 5 sin(theta)= 5 cos(theta). What do you get if you divide both sides by 5 cos(theta)?

## 1. What are polar coordinates?

Polar coordinates are a system of representing points in a two-dimensional space using a distance from the origin and an angle from a fixed reference direction.

## 2. How do you find the intersection of two polar coordinates?

To find the intersection of two polar coordinates, you can convert them to Cartesian coordinates and then use the standard method of finding the intersection of two lines.

## 3. Can polar coordinates be used to represent three-dimensional points?

No, polar coordinates are only used to represent points in a two-dimensional space. To represent points in a three-dimensional space, you would need to use spherical coordinates.

## 4. What is the difference between polar coordinates and Cartesian coordinates?

The main difference between polar coordinates and Cartesian coordinates is the way they represent points. Polar coordinates use distance and angle from the origin, while Cartesian coordinates use horizontal and vertical distances from the origin.

## 5. How are polar coordinates used in real-world applications?

Polar coordinates are commonly used in navigation and mapping systems, as well as in physics and engineering to describe the position of objects in a circular or rotational motion. They are also used in polar graphs and equations to represent curves and shapes.

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