Precalculus Chapter 9 Review

Front

What is the polar coordinate representation of the point (5, π)?

Back

The polar coordinate (5, π) represents the point (5, 180°) in rectangular coordinates.

Front

Convert the polar point (6, \frac{2\pi}{3}) into rectangular form.

Back

The rectangular form is (-3, 3\sqrt{3}).

Front

What is the polar equation for the circle defined by the rectangular equation x² + y² = 25?

Back

The polar equation is r = 5.

Front

Which letter represents the point (2, \frac{\pi}{6})?

Back

The point (2, \frac{\pi}{6}) is represented by B.

Front

Find the polar coordinates for the point (-2, -2).

Back

The polar coordinates are (2.83, 225°).

Front

Define polar coordinates.

Back

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

Front

What is the relationship between polar and rectangular coordinates?

Back

The relationship is given by: x = r cos(θ) and y = r sin(θ).

Front

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

Back

Use the formulas: r = √(x² + y²) and θ = tan⁻¹(y/x).

Front

What is the formula for converting polar coordinates to rectangular coordinates?

Back

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

Front

What is the significance of the angle in polar coordinates?

Back

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