# The tugboat Lawowa is returning to port for the day. It has a speed of 7.00 knots. The heading to...

## Question:

The tugboat Lawowa is returning to port for the day. It has a speed of 7.00 knots. The heading to the Lawowa's port is 33.0 degrees west of north. If due east is 0, what is the tug's heading as a vector in polar notation?

## Polar Coordinates

The polar coordinate system is a two-dimensional system identifying a point by two coordinates: the distance from the origin {eq}r {/eq} and an angle of the line connecting the origin with the point to a horizontal axis {eq}\theta {/eq}. Cartesian coordinates {eq}\langle x,y \rangle {/eq} and polar coordinates {eq}\langle r,\theta \rangle {/eq} of one and the same point are related as: \begin{align*} x &= r \, \cos \theta \\ y &= r \, \sin \theta \end{align*}

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