11.7 Day 1 Cylindrical Coordinates

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11.7 Day 1 Cylindrical Coordinates. Comparing Cartesian and cylindrical coordinates. Note: these are just polar coordinates with a z coordinate (z is a vertical component). Conversion formulas from cylindrical to rectangular coordinates. - PowerPoint PPT Presentation

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<ul><li><p>11.7 Day 1 Cylindrical Coordinates</p></li><li><p>Comparing Cartesian and cylindrical coordinates</p></li><li><p>Note: these are just polar coordinates with a z coordinate (z is a vertical component)</p></li><li><p>Conversion formulas from cylindrical to rectangular coordinates</p></li><li><p>Converting between cylindrical coordinates and rectangular (Cartesian)Note: these formulas must be memorized</p></li><li><p>Example 1 Convert the point (r, , z) = (4, 5/6, 3) to rectangular coordinates.</p></li><li><p>Solution to example 1</p></li><li><p>Example 2 _Convert the point (x, y, z) = (1, 3 , 2)to cylindrical coordinates.</p></li><li><p>Cylindrical coordinates are usually more convenient for representing cylindrical surfaces as they often result in simpler equations.</p></li><li><p>Vertical planes containing the z-axis and horizontal planes also have simple cylindrical coordinate equations</p></li><li><p>Example 3 a Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:</p></li><li><p>Solution to 3aFrom the preceding section, you know that x2 + y2 = 4z2 is a double napped cone with its axis along the z-axis as shown.</p><p>If you replace x2 + y2 with r2, the equation in cylindricalCoordinates is r2 = 4z2</p><p>x2 + y2 = 4z2 Rectangular equation</p><p>r2 = 4z2 Cylindrical equation</p></li><li><p>Example 3bFind an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:</p></li><li><p>Solution to 3b</p></li><li><p>Example 4Find an equation in rectangular coordinates for the surface represented by the cylindrical equation:Identify the surface</p><p>r2cos2 +z2 +1 = 0</p></li><li><p>yzx</p></li><li><p>Changing between coordinates on the TI 89Press 2nd 5 (math) 4 matrices L Vecor opsTo polar, to cynd To convert rectangular to Polar (2 D) or cylindrical (3D)[1,2] to Polar (to expressed with a triangle)[1,2,3] to Cylind</p></li><li><p>Bonus material on the next slidesThis is a polar bear in rectangular formNote: Homework do the assignment sheet plus the activity on the class website.</p></li><li><p>Need Help?If you are ever in need of assistance type in the following equation:</p><p>See the next slide</p></li><li><p>Help is on the way</p></li></ul>

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