Question

a point is located in a polar coordinate system by the coordinates r= 5.6 m and angle = 10 degrees. find the x and y coordinates of this point, assuming that the two coordinate systems have the same origin.

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Cristian

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To find the x and y coordinates of a point in a polar coordinate system, we can use the following formulas:

x = r \cos(\theta)

y = r \sin(\theta)

Given that the radius (r) is 5.6 m and the angle (\theta) is 10 degrees, we can substitute these values into the formulas to find the x and y coordinates:

x = 5.6 \cos(10^\circ)

y = 5.6 \sin(10^\circ)

Now we can calculate the x and y coordinates:

x\approx5.6\times0.9848\approx5.51\,\text{m}

y\approx5.6\times0.1736\approx0.97\text{m}

Therefore, the x-coordinate is approximately 5.51 m and the y-coordinate is approximately 0.97 m.

Answer: The x-coordinate is approximately 5.51 m and the y-coordinate is approximately 0.97 m.

Given that the radius (r) is 5.6 m and the angle (\theta) is 10 degrees, we can substitute these values into the formulas to find the x and y coordinates:

Now we can calculate the x and y coordinates:

Therefore, the x-coordinate is approximately 5.51 m and the y-coordinate is approximately 0.97 m.

Answer: The x-coordinate is approximately 5.51 m and the y-coordinate is approximately 0.97 m.

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