Polar Review

Front

What is the average rate of change of a function f between two angles?

Back

Front

What is the polar coordinate representation of a point?

Back

A point in polar coordinates is represented as (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis.

Front

How do you convert polar coordinates to rectangular coordinates?

Back

To convert from polar to rectangular coordinates, use the formulas: \( x = r \cos(\theta) \) and \( y = r \sin(\theta) \).

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in the interval, if x1 < x2 then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in the interval, if x1 < x2 then f(x1) > f(x2).

Front

What is the significance of the pole in polar coordinates?

Back

The pole in polar coordinates is the origin point (0,0), from which all points are measured in terms of distance (r) and angle (θ).

Front

How do you determine if the distance from a point to the pole is increasing or decreasing?

Back

To determine if the distance from a point to the pole is increasing or decreasing, analyze the derivative of the distance function with respect to θ.

Front

What is the relationship between polar and rectangular coordinates?

Back

Polar coordinates (r, θ) can be converted to rectangular coordinates (x, y) using the relationships: \( x = r \cos(\theta) \) and \( y = r \sin(\theta) \).

Front

What is the formula for the average rate of change of a function f(θ)?

Back

The formula for the average rate of change of a function f(θ) between two angles θ1 and θ2 is: \( \frac{f(\theta_2) - f(\theta_1)}{\theta_2 - \theta_1} \).

Front

What is the polar coordinate of the point (3, 5π/3)?

Back

The polar coordinate (3, 5π/3) represents a point that is 3 units away from the pole at an angle of 5π/3 radians.