Polar Flashcard Review(no limacons)

Front

What is the polar coordinate representation of the point (x, y) in rectangular coordinates?

Back

The polar coordinates (r, θ) can be found using the formulas: r = √(x² + y²) and θ = arctan(y/x).

Front

How do you convert polar coordinates to rectangular coordinates?

Back

To convert (r, θ) to rectangular coordinates (x, y), use the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

What is the polar form of the point (√8, √8)?

Back

The polar form is (-4, \frac{5\pi}{4}).

Front

What is the equation of a circle in polar coordinates?

Back

The equation of a circle in polar coordinates is r = a, where 'a' is the radius.

Front

What does the equation r = sin(θ) represent in polar coordinates?

Back

It represents a circle with a radius of 0.5 centered at (0, 0.5) in rectangular coordinates.

Front

How do you identify the graph of r = 4 sin(θ)?

Back

This equation represents a circle with a radius of 2 centered at (0, 2) in rectangular coordinates.

Front

What is the relationship between polar and rectangular coordinates?

Back

Polar coordinates (r, θ) relate to rectangular coordinates (x, y) through the equations: x = r * cos(θ) and y = r * sin(θ).

Front

What is the significance of the angle θ in polar coordinates?

Back

The angle θ represents the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Front

How do you convert the polar equation r = 4 sin(θ) to rectangular form?

Back

The rectangular form is x² + (y - 2)² = 4.

Front

What does the equation r = -3cos(θ) represent?

Back

It represents a circle with a radius of 3 centered at (1.5, 0) in rectangular coordinates.