Polar Angles

Front

What is a polar angle?

Back

A polar angle is the angle measured from the positive x-axis in a polar coordinate system, typically denoted as \( \theta \). It is used to specify the direction of a point in a two-dimensional plane.

Front

What is the range of polar angles?

Back

The range of polar angles is from 0 degrees to 360 degrees (or 0 to 2\(\pi\) radians).

Front

How do you convert polar angles to Cartesian coordinates?

Back

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

Front

What is the polar angle for the point (0, 1)?

Back

The polar angle for the point (0, 1) is 90 degrees, as it lies on the positive y-axis.

Front

What is the polar angle for the point (-1, 0)?

Back

The polar angle for the point (-1, 0) is 180 degrees, as it lies on the negative x-axis.

Front

What is the polar angle for the point (1, 1)?

Back

The polar angle for the point (1, 1) is 45 degrees, calculated using \( \theta = \tan^{-1}(\frac{y}{x}) = \tan^{-1}(1) \).

Front

What is the polar angle for the point (1, -1)?

Back

The polar angle for the point (1, -1) is 315 degrees, calculated using \( \theta = \tan^{-1}(\frac{y}{x}) = \tan^{-1}(-1) \) and adjusting for the fourth quadrant.

Front

What is the significance of a 0-degree polar angle?

Back

A 0-degree polar angle indicates a point located on the positive x-axis in the polar coordinate system.

Front

What is the significance of a 90-degree polar angle?

Back

A 90-degree polar angle indicates a point located on the positive y-axis in the polar coordinate system.

Front

What is the significance of a 180-degree polar angle?

Back

A 180-degree polar angle indicates a point located on the negative x-axis in the polar coordinate system.