Polar Curves Checkpoint

Front

What is the equation of a circle in polar coordinates?

Back

r = a, where 'a' is the radius.

Front

How do you convert polar coordinates (r, θ) to rectangular coordinates (x, y)?

Back

x = r * cos(θ), y = r * sin(θ).

Front

What is the polar coordinate representation of the point (-3, 0)?

Back

(3, π).

Front

What is the equation for a rose curve with 'n' leaves?

Back

r = a * sin(nθ) or r = a * cos(nθ), where 'n' determines the number of leaves.

Front

How do you convert rectangular coordinates (x, y) to polar coordinates (r, θ)?

Back

r = √(x² + y²), θ = arctan(y/x).

Front

What is the polar equation for a limacon with an inner loop?

Back

r = a + b * sin(θ) or r = a + b * cos(θ), where |b| > |a|.

Front

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

Back

It represents the direction of the point from the origin.

Front

What is the polar equation for a circle centered at the origin?

Back

r = a, where 'a' is the radius.

Front

How do you identify the number of leaves in a rose curve?

Back

If 'n' is odd, it has 'n' leaves; if 'n' is even, it has '2n' leaves.

Front

What is the polar coordinate for the point (6√3, 6)?

Back

(12, π/6).