Ch 15

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Calculus

AP Calculus BC

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10 Terms

1
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What is the transformation from Cartesian to cylindrical coordinates for x?

x = r * cos(theta)

2
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What is the transformation from Cartesian to cylindrical coordinates for y?

y = r * sin(theta)

3
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What is the transformation from Cartesian to cylindrical coordinates for z?

z = z (remains the same)

4
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What is the formula for r in cylindrical coordinates?

r = sqrt(x^2 + y^2)

5
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What is the formula for theta in cylindrical coordinates?

theta = atan2(y, x)

6
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What is the transformation from Cartesian to spherical coordinates for x?

x = p * sin(phi) * cos(theta)

7
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What is the transformation from Cartesian to spherical coordinates for y?

y = p * sin(phi) * sin(theta)

8
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What is the transformation from Cartesian to spherical coordinates for z?

z = p * cos(phi)

9
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What is the formula for p in spherical coordinates?

p = sqrt(x^2 + y^2 + z^2)

10
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What is the formula for phi in spherical coordinates?

phi = acos(z / p)