C1.3

determine, using trigonometric relationships [e.g., $x=r\cos \theta$, $y=r\sin \theta$, $\theta ={\tan }^{-1}\left(\frac{y}{x}\right)$ or ${\tan }^{-1}\left(\frac{y}{x}\right)+180^{\circ }$, $r=\sqrt{x^2+y^2}$], the Cartesian representation of a vector in two-space given as a directed line segment, or the representation as a directed line segment of a vector in two-space given in Cartesian form [e.g., representing the vector $(8,6)$ as a directed line segment] Sample problem: Represent the vector with a magnitude of 8 and a direction of $30^{\circ }$ anticlockwise to the positive x-axis in Cartesian form.