Converting Rectangular Equations to Polar Form

The video tutorial explains how to convert a linear equation from rectangular form to polar form. It begins by introducing the equation 3x - 2y = 6 and the need to substitute x and y with r and theta using the equations x = r cos(theta) and y = r sin(theta). After substitution, the tutorial demonstrates factoring out r and solving the equation for r, resulting in the polar equation r = 6 / (3 cos(theta) - 2 sin(theta)). The tutorial concludes with a summary of the conversion process.

What is the initial form of the equation we are converting?

• x - y = 6

• 2x - 3y = 6

• 3x - 2y = 6

• 3x + 2y = 6

What is the first step in converting a rectangular equation to polar form?

• Substitute x and y

• Divide by a trigonometric function

• Solve for y

• Factor out r

Which equations are used to substitute x and y in terms of r and θ?

• x = r sin(θ), y = r cos(θ)

• x = r cos(θ), y = r sin(θ)

• x = r sec(θ), y = r csc(θ)

• x = r tan(θ), y = r cot(θ)

Which trigonometric functions are used in the substitution process?

• Sine and cosine

• Tangent and cotangent

• Secant and cosecant

• Sine and tangent

After substitution, what common factor is identified in the polar equation?

• r

• cos(θ)

• sin(θ)

• θ

What operation is performed to isolate r in the polar equation?

• Division

• Addition

• Multiplication

• Subtraction

What is the final polar equation derived from 3x - 2y = 6?

• r = 6 / (3 sin(θ) - 2 cos(θ))

• r = 6 / (3 cos(θ) + 2 sin(θ))

• r = 6 / (3 cos(θ) - 2 sin(θ))

• r = 6 / (2 cos(θ) - 3 sin(θ))

What is the purpose of converting a rectangular equation to polar form?

• To solve for x and y

• To change the coordinate system

• To eliminate variables

• To simplify calculations