- #1

tatiana

- 43

- 1

*A point on a polar coordinate system is located at r=2.0 and = 25 degrees.*

& then how you would use the Pythagorean Theorem to verify your answer?

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- Thread starter tatiana
- Start date

In summary, to find a point in cartesian coordinates based on polar coordinates, you need to use sines and cosines to determine the corresponding x and y values. Then, plug these values into the Pythagorean Theorem with r as the hypotenuse to verify the answer. In general, x = rcos(a) and y = rsin(a) for any given polar coordinates (r, a).

- #1

tatiana

- 43

- 1

& then how you would use the Pythagorean Theorem to verify your answer?

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- #2

Dr Lots-o'watts

- 646

- 0

Then r is always the hypotenuse so you can plug it into the Pythagorean Theorem with the x and y you just found: x^2 + y^2 = r^2.

- #3

mathman

Science Advisor

- 8,140

- 572

In general if you are given something in polar coordinates (r,a) then x=rcos(a) and y=rsin(a).

Cartesian coordinates are a system of coordinates used to locate a point on a plane or in space. They were developed by French mathematician René Descartes in the 17th century and are named after him.

To solve for Cartesian coordinates, you need to know the x and y values of a point on a plane. The x value represents the horizontal distance from the origin (usually denoted as 0), while the y value represents the vertical distance. You can use the Pythagorean theorem to calculate the distance from the origin to the point, and then use trigonometric functions to determine the angle between the point and the x-axis.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In Cartesian coordinates, this theorem is used to calculate the distance from the origin to a point, which is the hypotenuse of a right triangle formed by the x and y values.

To verify Cartesian coordinates, you can use the Pythagorean theorem to calculate the distance from the origin to the point. Then, you can use the calculated distance and the angle between the point and the x-axis to find the x and y values using trigonometric functions. If the calculated x and y values match the given coordinates, then the coordinates are verified.

Cartesian coordinates are used in a wide variety of fields, including mathematics, physics, engineering, and navigation. They are essential for graphing and representing data, as well as for describing the location of objects in space. They are also used in computer graphics and in GPS systems to determine the location of a person or object on a map.

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