Convert polar equation of a circle to rectangular equation

The video tutorial discusses solving a mathematical problem involving trigonometric functions and equations. The teacher explains why certain methods, like multiplying by sine, are not ideal due to complications with sine squared terms. Instead, the teacher demonstrates multiplying by R to simplify the equation, leading to a form that can be solved by completing the square. This process reveals the equation of a circle with a specific radius and center. The tutorial concludes with a visualization of the solution and a recap of the key steps involved.

Why does the speaker avoid multiplying by sine to eliminate Y in the polar equation?

• It would make the equation linear, which is not desired.

• It would result in a sine squared term, complicating the equation.

• It would eliminate all variables, leaving no equation.

• It would convert the equation into a hyperbola.

What is the result of multiplying both sides of the equation by R?

• An equation with no solution.

• An equation representing a circle.

• A linear equation in X and Y.

• A quadratic equation in R.

What mathematical technique is reintroduced to simplify the equation?

• Differentiation

• Integration

• Factoring

• Completing the square

What is the center of the circle described by the equation after completing the square?

• (0, 3)

• (3, 0)

• (0, 0)

• (3, 3)

What is the radius of the circle obtained from the equation?

• 5

• 4

• 3

• 2