The polar coordinates of a certain point are (r = 3.00 cm, theta = 211 degree).

Question

The polar coordinates of a certain point are (r = 3.00 cm, theta = 211 degree). (a) Find its Cartesian coordinates x and y. x = 2.57 The response you submitted has the wrong sign. cm y = -1.55 cm (b) Find the polar coordinates of the points with Cartesian coordinates (-x, y). r = 3 cm theta = 211.11 Your response differs from the correct answer by more than 100%. degree (c) Find the polar coordinates of the points with Cartesian coordinates (-2x, -2y). r = 6.02 cm theta = 148.56 Your response differs from the correct answer by more than 100%.degree (d) Find the polar coordinates of the points with Cartesian coordinates (3x, -3y). r = 4.16 Your response differs from the correct answer by more than 10%. Double check your calculations. cm theta = 48.18 Your response differs from the correct answer by more than 10%. Double check your calculations. degree

Explanation / Answer

First part

(a) x = r*cos theta = 3.0*cos211 = - 2.57 cm

y = r*sin theta = 3.0*sin211 = -1.55 cm

(b) cartesian cordinates (-x, y) = (2.57, -1.55)

r = sqrt[2.57^2 + 1.55^2] = 3.0

theta = 360 - tan^-1(1.55/2.57) = 329 deg

(c) (-2x, -2y) = (5.14, 3.1)

theta = tan^-1(3.1 / 5.14) = 31.1 deg

(d) (3x, -3y) = (-7.71, 4.65)

r = sqrt[7.71^2 + 4.65^2] = 9.0

theta = 90 + tan^-1(4.65/7.71) = 90 + 31 = 121 deg

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