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Convert the rectangular coordinates of each point to polar coordinates. Use degrees for 0. 5. (√3,3) 9. (4,4) x² + y² = r²

Convert the rectangular coordinates of each point to polar coordinates. Use degrees for 0. 5. (√3,3) 9. (4,4) x² + y² = r²

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 3E
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**Converting Rectangular Coordinates to Polar Coordinates** **Instructions:** Convert the rectangular coordinates of each point to polar coordinates. Use degrees for θ. 1. \( (\sqrt{3}, 3) \) 2. \( (-2, 2) \) 3. \( (0, 2) \) 4. \( (-3, -3) \) 5. \( (4, 4) \) 6. \( (-2, 2\sqrt{3}) \) **Formulas:** \[ x^2 + y^2 = r^2 \] \[ \tan \theta = \frac{y}{x} \] **Example:** **Sketch the graph of the polar equation \( r = 2 \cos \theta \)** **Step 1 => Create table** \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \theta & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ & 120^\circ & 135^\circ & 150^\circ & 180^\circ \\ \hline r & & & & & & & & & \\ \hline \end{array} \] **Step 2 => Plot points and draw curve** **Explanation of Diagram:** The diagram below the steps illustrates the graph of the polar equation \( r = 2 \cos \theta \). The horizontal x-axis and vertical y-axis guide the placement of these points. Various points are plotted such as: - \( r = 2, \theta = 0^\circ \) at (2, 0) - \( r = \sqrt{3}, \theta = 30^\circ \) at \((\sqrt{3}, 30^\circ)\) - \( r = 1, \theta = 60^\circ \) at (1, 60^\circ) - \( r = 0, \theta = 90^\circ \) at (0, 90^\circ) The points are joined to reveal the curve described by the polar equation \( r = 2 \cos \theta \).
Transcribed Image Text:**Converting Rectangular Coordinates to Polar Coordinates** **Instructions:** Convert the rectangular coordinates of each point to polar coordinates. Use degrees for θ. 1. \( (\sqrt{3}, 3) \) 2. \( (-2, 2) \) 3. \( (0, 2) \) 4. \( (-3, -3) \) 5. \( (4, 4) \) 6. \( (-2, 2\sqrt{3}) \) **Formulas:** \[ x^2 + y^2 = r^2 \] \[ \tan \theta = \frac{y}{x} \] **Example:** **Sketch the graph of the polar equation \( r = 2 \cos \theta \)** **Step 1 => Create table** \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \theta & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ & 120^\circ & 135^\circ & 150^\circ & 180^\circ \\ \hline r & & & & & & & & & \\ \hline \end{array} \] **Step 2 => Plot points and draw curve** **Explanation of Diagram:** The diagram below the steps illustrates the graph of the polar equation \( r = 2 \cos \theta \). The horizontal x-axis and vertical y-axis guide the placement of these points. Various points are plotted such as: - \( r = 2, \theta = 0^\circ \) at (2, 0) - \( r = \sqrt{3}, \theta = 30^\circ \) at \((\sqrt{3}, 30^\circ)\) - \( r = 1, \theta = 60^\circ \) at (1, 60^\circ) - \( r = 0, \theta = 90^\circ \) at (0, 90^\circ) The points are joined to reveal the curve described by the polar equation \( r = 2 \cos \theta \).
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