11.7 day 1 cylindrical coordinates
Post on 20-Mar-2016
Embed Size (px)
DESCRIPTION11.7 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
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
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