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Find the cartesian coordinates of the given polar coordinates (-2, 5/4). Then plot the point.

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Final Answer:

The Cartesian coordinates of the given polar coordinates (-2, 5/4) are (2√2, -2√2).

Step-by-step explanation:

To convert the polar coordinates (-2, 5/4) to Cartesian coordinates, we use the formulas x = r * cos(θ) and y = r * sin(θ), where r is the radius and θ is the angle in radians. In this case, r = -2 and θ = 5/4. Substituting these values into the formulas, we get x = -2 * cos(5/4) and y = -2 * sin(5/4). Evaluating these trigonometric functions gives us x = 2√2 and y = -2√2. Therefore, the Cartesian coordinates of the given polar coordinates are (2√2, -2√2).

Converting polar coordinates to Cartesian coordinates involves using trigonometric functions to find the x and y values corresponding to the given radius and angle. In this case, we utilized the formulas x = r * cos(θ) and y = r * sin(θ) to perform the conversion. By substituting the given values of r and θ into these formulas and evaluating the trigonometric functions, we obtained the Cartesian coordinates (2√2, -2√2) for the given polar coordinates (-2, 5/4).

Plotting the point with Cartesian coordinates (2√2, -2√2) on a graph would place it in the third quadrant, as both x and y are negative. This point represents the same position as the given polar coordinates (-2, 5/4), but in a different coordinate system.

User Shankar Gupta
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