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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  • 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

  • Converting between cylindrical coordinates and rectangular (Cartesian)Note: these formulas must be memorized

  • Example 1 Convert the point (r, , z) = (4, 5/6, 3) to rectangular coordinates.

  • Solution to example 1

  • Example 2 _Convert the point (x, y, z) = (1, 3 , 2)to cylindrical coordinates.

  • Cylindrical coordinates are usually more convenient for representing cylindrical surfaces as they often result in simpler equations.

  • Vertical planes containing the z-axis and horizontal planes also have simple cylindrical coordinate equations

  • Example 3 a Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:

  • 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.

    If you replace x2 + y2 with r2, the equation in cylindricalCoordinates is r2 = 4z2

    x2 + y2 = 4z2 Rectangular equation

    r2 = 4z2 Cylindrical equation

  • Example 3bFind an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:

  • Solution to 3b

  • Example 4Find an equation in rectangular coordinates for the surface represented by the cylindrical equation:Identify the surface

    r2cos2 +z2 +1 = 0

  • yzx

  • 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

  • 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.

  • Need Help?If you are ever in need of assistance type in the following equation:

    See the next slide

  • Help is on the way

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