Question

What are the Cartesian coordinates of the point with polar coordinates 4π/3 and 5.50 m?

a) (2.75 m, 4.75 m)
b) (2.75 m, -4.75 m)
c) (-2.75 m, 4.75 m)
d) (-2.75 m, -4.75 m)

Answer 1

Answer:Now, substituting r = 5.50 m and θ = 4π/3 rad into our Cartesian coordinate transformation equations, we find: x = 5.50m * cos(4π/3rad) = -2.75m, y = 5.50m * sin(4π/3rad) = -4.77m. So, the Cartesian coordinates corresponding to the polar coordinates r = 5.50m and θ = 240° are approximately (-2.75m,-4.77m).

Step-by-step explanation:

Answer 2

To find the Cartesian coordinates of a point given its polar coordinates, use the formulas: x = r * cos(theta) and y = r * sin(theta). The Cartesian coordinates of the point with polar coordinates (4π/3, 5.50 m) are approximately (-2.75 m, -4.75 m).

Step-by-step explanation:

To convert polar coordinates to Cartesian coordinates, we can use the following formulas:

x = r * cos(theta)

y = r * sin(theta)

Given that the polar coordinates of the point are (4π/3, 5.50 m), we can substitute these values into the formulas to find the Cartesian coordinates:

x = (5.50 m) * cos(4π/3)

y = (5.50 m) * sin(4π/3)

After evaluating these expressions, we find that the Cartesian coordinates of the point are approximately (-2.75 m, -4.75 m), which corresponds to option d).