Converting Between Spherical and Rectangular Equations

This video tutorial covers the conversion between spherical and rectangular equations. It begins with an introduction to the concepts and equations used for conversion. The tutorial provides step-by-step instructions and examples for converting rectangular equations to spherical form and vice versa. Key concepts such as the use of trigonometric identities and coordinate transformations are explained. The video concludes with a summary of the conversion processes.

What are the key variables used in spherical equations?

• X, Y, Z

• Row, Theta, F

• A, B, C

• Alpha, Beta, Gamma

In the first example, what substitution is made for the variable 'x'?

• Row cos V

• Row sin Theta

• Row cos V sin Theta

• Row sin V cos Theta

What is the final form of the spherical equation in the first example?

• Row = 2 sin F cos Theta

• Row = 2 cose F sec Theta

• Row = 2 tan F

• Row = 2 sin Theta

In the second example, what is the initial rectangular equation given?

• x^2 + y^2 - z^2 = 0

• x^2 + y^2 = z^2

• x^2 + y^2 + z^2 = 0

• x^2 - y^2 + z^2 = 0

What angle is determined in the second example for the spherical equation?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

What is the value of Theta in the spherical equation converted to rectangular form in the fourth section?

• Pi / 2

• Pi / 4

• Pi / 6

• Pi

What is the rectangular form of the equation when Theta is Pi/4?

• Y = 2X

• Y = -X

• Y = X

• Y = X/2

In the final example, what geometric shape is identified after completing the square?

• Sphere

• Cone

• Cylinder

• Parabola

What is the center of the sphere identified in the final example?

• (0, 0, 0)

• (1, 0, 0)

• (0, 0, 1)

• (0, 1, 0)

What is the radius of the sphere identified in the final example?

• 1

• 2

• 3

• 4