Polar and Rectangular Coordinate Relationships

The video tutorial explains how to convert the rectangular equation y=3 into polar form. It begins by describing the graph of y=3 as a horizontal line intersecting the y-axis at 3. The tutorial then demonstrates the substitution of y with r sin(theta) to convert the equation into polar form, resulting in r = 3/sin(theta). It further simplifies the equation by expressing it as r = 3 cosecant(theta), eliminating the fraction. The video provides a clear step-by-step process for converting rectangular equations to polar form.

What is the graph of the equation y = 3 in rectangular coordinates?

• A vertical line intersecting the x-axis at 3

• A horizontal line intersecting the y-axis at 3

• A diagonal line through the origin

• A circle centered at the origin

Which equation relates y in rectangular coordinates to polar coordinates?

• y = r sec(θ)

• y = r sin(θ)

• y = r cos(θ)

• y = r tan(θ)

What substitution is made for y when converting y = 3 to polar form?

• r sin(θ)

• r tan(θ)

• r cos(θ)

• r sec(θ)

How do you solve the equation r sin(θ) = 3 for r?

• Multiply both sides by sin(θ)

• Divide both sides by sin(θ)

• Add sin(θ) to both sides

• Subtract sin(θ) from both sides

What is the polar equation for y = 3 after solving for r?

• r = 3 tan(θ)

• r = 3 / sin(θ)

• r = 3 cos(θ)

• r = 3 sin(θ)

What is the alternative form of the polar equation r = 3 / sin(θ)?

• r = 3 tan(θ)

• r = 3 csc(θ)

• r = 3 sec(θ)

• r = 3 cot(θ)

Why might one prefer to write the polar equation using cosecant?

• To simplify the graph

• To eliminate the fraction

• To make it a linear equation

• To avoid using sine

Which of the following is a correct polar equation for y = 3?

• r = 3 sec(θ)

• r = 3 csc(θ)

• r = 3 cos(θ)

• r = 3 tan(θ)