Question Part Points Submissions Used Example 3.1 Polar Coordinates Finding pola

Question

Question Part Points Submissions Used Example 3.1 Polar Coordinates Finding polar coordinates when Cartesian coordinates are given (not drawn to scale). The Cartesian coordinates of a point in the xy plane are (x, y)= (-2.10, -5.70) m as shown the figure. Find the polar coordinates of this point. SOLVE IT Conceptualize The drawing in the figure helps us conceptualize the problem. Categorize Based on the statement of the problem and the Conceptualize step, we recognize that weare simply converting from Cartesian coordinates to polar coordinates. We therefore categorize this example as a substitution problem. Substitution problems generally do not have an extensive Analyze step other than the substitution of numbers into a given equation. Similarly, the Finalize step consists primarily of checking the units and making sure that the answer is reasonable. Therefore, for substitution problems, we will not label Analyze or Finalize steps.

Use Equation 3.3 to find ?: tan ? = y x = -5.70 m -2.10 m = 2.71 ? = ?

Notice that you must use the signs of x and y to find that the point lies in the third quadrant of the coordinate system. That is, tan(?) = tan(? + 180?).

Explanation / Answer

polar cooridnate exist in the form

= rcos + rsin

r = sqrrot( {-2.10}^2 + {-5.70}^2) = 6.07 APPRX

TAN = -5.70/- 2.10 =

=249.775 degree apprx

polar cooridnates= x= 6.07cos249.775

y = 6.07sin249.775

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