Polar Coordinates

Front

What is the polar form of the equation r = tan θ sec θ?

Back

This equation represents a relationship between the radius (r) and the angle (θ) in polar coordinates, where r is expressed in terms of the tangent and secant functions.

Front

How do you convert the polar equation r = 2 to rectangular form?

Back

The rectangular form is x = 2, which indicates a vertical line at x = 2.

Front

What is the relationship between y and r in polar coordinates?

Back

y = rsinθ, where r is the radius and θ is the angle.

Front

How do you find the radius r given rectangular coordinates x = 12 and y = 5?

Back

Use the formula r = √(x² + y²). Here, r = √(12² + 5²) = 13.

Front

Convert the rectangular coordinates (x, y) = (√8, 7π/6) to polar form.

Back

The polar form is (r, θ) = (√8, 7π/6).

Front

What is the formula to convert rectangular coordinates (x, y) to polar coordinates (r, θ)?

Back

r = √(x² + y²) and θ = arctan(y/x).

Front

What does the term 'polar coordinates' refer to?

Back

Polar coordinates are a two-dimensional coordinate system where each point is determined by a distance from a reference point (the origin) and an angle from a reference direction.

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 express the point (3, π/4) in rectangular coordinates?

Back

x = r cos θ = 3 cos(π/4) = -√2, y = r sin θ = 3 sin(π/4) = √2.

Front

What is the polar coordinate for the point (0, 0) in rectangular coordinates?

Back

The polar coordinate is (0, θ) for any angle θ, since the radius is zero.