Answer
(a) $\theta = 333.4^{\circ}$
(b) $\theta = 26.6^{\circ}$
(c) $\theta = 153.4^{\circ}$
(d) $\theta = 206.6^{\circ}$
Work Step by Step
First we can find the angle $a$ that each vector makes with the x-axis.
$tan(a) = \frac{1.00}{2.00}$
$a = tan^{-1}(\frac{1.00}{2.00}) = 26.6^{\circ}$
Note that we are measuring $\theta$ counterclockwise from the +x-axis.
(a) $a$ is below the +x-axis and to the right of the -y-axis, therefore $\theta = 360^{\circ}-26.6^{\circ}= 333.4^{\circ}$.
(b) $a$ is above the +x-axis and to the right of the +y-axis, therefore $\theta = 26.6^{\circ}$.
(c) $a$ is above the -x-axis and to the left of the +y-axis, therefore $\theta = 180^{\circ}-26.6^{\circ}= 153.4^{\circ}$.
(d) $a$ is below the -x-axis and to the left of the -y-axis, therefore $\theta = 180^{\circ}+26.6^{\circ}= 206.6^{\circ}$.
