2021 Unit 6 Review

Front

What is the distance formula in a coordinate plane?

Back

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Front

How do you convert rectangular coordinates to polar coordinates?

Back

To convert from rectangular coordinates \((x, y)\) to polar coordinates \((r, \theta)\): 1. Calculate \(r = \sqrt{x^2 + y^2}\). 2. Calculate \(\theta = \tan^{-1}(\frac{y}{x})\).

Front

What is a polar equation?

Back

A polar equation expresses a relationship between the radius \(r\) and the angle \(\theta\) in polar coordinates.

Front

What is the general form of a polar equation?

Back

The general form of a polar equation can be expressed as \(r = f(\theta)\), where \(f(\theta)\) is a function of \(\theta\).

Front

What is the significance of the angle in polar coordinates?

Back

The angle \(\theta\) in polar coordinates indicates the direction of the point from the origin.

Front

What is a limacon in polar coordinates?

Back

A limacon is a type of polar graph that can have an inner loop, and is represented by equations of the form \(r = a + b \sin(\theta)\) or \(r = a + b \cos(\theta)\).

Front

What does the equation \(r = 6 + 6 \sin(\theta)\) represent?

Back

This equation represents a limacon with an inner loop.

Front

How do you identify a line in polar coordinates?

Back

A line in polar coordinates can be represented by equations of the form \(\theta = k\), where \(k\) is a constant angle.

Front

What is the relationship between parametric equations and graphs?

Back

Parametric equations define a curve by expressing the coordinates as functions of a parameter, often time, allowing for the representation of complex shapes.

Front

How do you convert polar coordinates back to rectangular coordinates?

Back

To convert from polar coordinates \((r, \theta)\) to rectangular coordinates \((x, y)\): 1. Calculate \(x = r \cos(\theta)\). 2. Calculate \(y = r \sin(\theta)\).