Converting Polar and Rectangular Coordinates

Front

What are polar coordinates?

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 (usually the positive x-axis).

Front

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

Back

The conversion formulas are: x = r * cos(θ) and y = r * sin(θ).

Front

What is the rectangular coordinate of the polar point (6, 150°)?

Back

(-3√3, 3) is the rectangular coordinate of the polar point (6, 150°).

Front

Convert the polar coordinates (6, 2π/3) to rectangular coordinates.

Back

The rectangular coordinates are (-3, 3√3).

Front

What is the rectangular coordinate of the polar point (20, 11π/6)?

Back

The rectangular coordinates are (10√2, -10).

Front

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

Back

The formulas are: r = √(x² + y²) and θ = arctan(y/x).

Front

What is the significance of the angle in polar coordinates?

Back

The angle in polar coordinates indicates the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Front

What is the relationship between radians and degrees?

Back

Radians and degrees are two units for measuring angles; 180° is equivalent to π radians.

Front

How do you simplify √32?

Back

√32 simplifies to 4√2.

Front

What is the polar coordinate representation of the point (0, -1) in rectangular coordinates?

Back

The polar coordinates are (1, 270°) or (1, 3π/2).