Goal Understand how to convert from plane rectangular coordinates to plane polar

Question

Goal Understand how to convert from plane rectangular coordinates to plane polar coordinates and vice versa. The Cartesian coordinates of a point in the xy-plane are (x, y) (-3.50 m, -2.50 m), as shown in the figure. Find the polar coordinates of this point. Convert (r, theta) = (5.00 m, 37.0 degree) to rectangular coordinates. Strategy Apply the trigonometric functions and their inverses, together with the Pythagorean theorem. Cartesian to Polar Take the squareroot of both sides of the equation to find the radial coordinate. Use the tangent function to find the angle with the inverse tangent, adding 180 degree because the angle is actually in third quadrant. Polar to Cartesian Use the trigonometric definition equations When we take up vectors in two dimensions, we will routinely use a similar process to find the direction and magnitude of a given vector from its components, or, conversely, to find the components from the vector's magnitude and direction. If you start with the answers in part (b) and work backwards to recover the radius and angle, there will be slight differences from the original quantities. What caused this difference? (Select all that apply.)

Explanation / Answer

If we start with the answers in part (b) and work backwards to recover the radius and angle, then there will be slight differences from the original quantities.

What caused this difference?

(a) Using inconsistent equations in doing the calculation in both directions.

(c) Rounding the value of tangent of an angle before taking its cosine in the example.

(d) Keeping more than three significant figures in an intermediate steps of each calculation.

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