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What is the conversion formula from polar to Cartesian coordinates?

The conversion formula from polar to Cartesian coordinates is x = r cos(theta) and y = r sin(theta).

To convert from polar to Cartesian coordinates, we need to use the trigonometric functions cosine and sine. In polar coordinates, a point is represented by an angle theta and a distance r from the origin. In Cartesian coordinates, a point is represented by its x and y coordinates.

To find the x coordinate, we use the formula x = r cos(theta). This formula tells us that the x coordinate is equal to the radius multiplied by the cosine of the angle. To find the y coordinate, we use the formula y = r sin(theta). This formula tells us that the y coordinate is equal to the radius multiplied by the sine of the angle.

For example, let's say we have a point in polar coordinates with an angle of 45 degrees and a radius of 2. To convert this to Cartesian coordinates, we first use the formula x = r cos(theta). Plugging in the values, we get x = 2 cos(45) = 2/sqrt(2) = sqrt(2). Next, we use the formula y = r sin(theta). Plugging in the values, we get y = 2 sin(45) = 2/sqrt(2) = sqrt(2). Therefore, the point in Cartesian coordinates is (sqrt(2), sqrt(2)).

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