11.7 Day 1 Cylindrical Coordinates
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Transcript of 11.7 Day 1 Cylindrical Coordinates
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11.7 Day 1 Cylindrical Coordinates
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Comparing Cartesian and cylindrical coordinates
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Note: these are just polar coordinates with a z coordinate (z is a vertical component)
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Conversion formulas from cylindrical to rectangular
coordinates
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Converting between cylindrical coordinates and
rectangular (Cartesian)Note: these formulas must be memorized
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Example 1
Convert the point (r, ө, z) = (4, 5π/6, 3) to rectangular coordinates.
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Solution to example 1
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Example 2
_Convert the point (x, y, z) = (1, √3 , 2)to cylindrical coordinates.
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Cylindrical coordinates are usually more convenient for representing cylindrical surfaces as they often result in simpler
equations.
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Vertical planes containing the z-axis and horizontal planes also have simple
cylindrical coordinate equations
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Example 3 a
Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:
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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
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Example 3b
Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:
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Solution to 3b
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Example 4Find an equation in rectangular coordinates for the surface
represented by the cylindrical equation:Identify the surface
r2cos2θ +z2 +1 = 0
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y
z
x
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Changing between coordinates on the TI 89
Press 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
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Bonus material on the next slides
This is a polar bear in rectangular form
Note: Homework do the assignment sheet plus the activity on the class website.
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