# 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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