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## Q. 1.2

Calculate the directions of the vectors in Example 1.

## Verified Solution

We depict these five vectors in Figure 5.

(a) Here v is in the first quadrant, and since $\tan \theta=2 / 2=1, \theta=\pi / 4$.
(b) Here $\theta=\tan ^{-1} 2 \sqrt{3} / 2=\tan ^{-1} \sqrt{3}=\pi / 3$.
(c) We see that $\mathbf{v}$ is in the second quadrant, and since $\tan ^{-3} 2 /(2 \sqrt{3})=\tan ^{-1} 1 / \sqrt{3}=\pi / 6$, we see from the figure that

$\theta=\pi-(\pi / 6)=5 \pi / 6$
(d) Here v is in the third quadrant, and since $\tan ^{-1} 1=\pi / 4, \theta=\pi+(\pi / 4)=5 \pi / 4$
(e) Since $\mathbf{v}$ is in the fourth quadrant, and since $\tan ^{-1}(-1)=-\pi / 4$, $\theta=2 \pi-(\pi / 4)=7 \pi / 4$