# Chilly vectors

**Classical Mechanics**Level 4

The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is polar coordinates (r,\(\theta\)), where r is the distance from the origin and \(\theta\) is the angle counterclockwise from the positive horizontal axis. Consider the vector \(\vec{v}\) with components \((0,1)\) in polar coordinates. Unlike the \((0,1)\) vector in Cartesian coordinates the direction of \(\vec{v}\) changes depending on the angular coordinate of the point at which the vector is at. This is due to the fact that there is a \(1\) in the \(\theta\) direction. Since the vector has no radial component, it always is tangent to the circle (points in the direction of increasing angle). For what value of \(\theta\) in **degrees** is \(\vec{v}\) parallel to the positive direction along the x-axis?