Converting Polar Coordinates to Cartesian Coordinates

In summary, Cartesian coordinates, or rectangular coordinates, are a way of representing points in a two-dimensional or three-dimensional space using numerical values for horizontal and vertical distances from a fixed reference point. They were invented by French philosopher and mathematician René Descartes and are essential in various fields of mathematics and science. To plot a point using Cartesian coordinates, the x and y (and z for three-dimensional space) coordinates are identified and plotted on corresponding axes. Other coordinate systems, such as polar, cylindrical, and spherical coordinates, are also used in mathematics and science for different purposes.
  • #1
chocolatelover
239
0

Homework Statement


The polar coordinates of a point are r=6.00 m and theta 250. What are the Cartesian coordinates?

X=?
Y=?


Homework Equations



Cos=adj./hyp.
sin=opp./hyp

The Attempt at a Solution



Would I just need to calculate the cos and sin? That is, I would just do sin 250=y/adj and solve for y, right?

Thank you very much
 
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  • #2
right.
x=rcos(theta)
y=rsin(theta)
 
  • #3
Thank you very much

Regards
 

FAQ: Converting Polar Coordinates to Cartesian Coordinates

What are Cartesian coordinates?

Cartesian coordinates, also known as rectangular coordinates, are a system of representing points in a two-dimensional or three-dimensional space using two or three numerical values, respectively. These values, known as x and y (and z for three-dimensional space), represent the horizontal and vertical distances of a point from a fixed reference point, known as the origin.

Who invented Cartesian coordinates?

Cartesian coordinates were invented by French philosopher and mathematician René Descartes in the 17th century. The system was named after him and is also known as the "Cartesian coordinate system."

What is the significance of Cartesian coordinates?

Cartesian coordinates are essential in the field of mathematics and science as they provide a standardized way to represent points in a space. This allows for precise measurements and calculations, making it easier to solve complex problems in various fields such as physics, engineering, and computer graphics.

How do you plot a point using Cartesian coordinates?

To plot a point on a Cartesian coordinate system, you need to identify the x and y (and z for three-dimensional space) coordinates of the point and then plot them on the corresponding axes. The point will be located at the intersection of the two axes, with its position determined by the values of its coordinates.

Are there any other coordinate systems besides Cartesian coordinates?

Yes, there are several other coordinate systems used in mathematics and science, such as polar coordinates, cylindrical coordinates, and spherical coordinates. Each system has its own unique way of representing points in a space and is used for different purposes.

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