Question

Let v = ⟨-5, 12⟩. What is the approximate direction angle of v?

23°
67°
113°
157°

Answer 1

It's C

Explanation:

Answer 2

C) 113°

Explanation:

The direction angle for a position vector
`v=\langle x,y\rangle` is
`\alpha=tan^(-1)((y)/(x))` plus a correction based on the quadrant (more on that later).

Hence:

`\theta=tan^(-1)((y)/(x))\\\\\theta=tan^(-1)((12)/(-5))\\\\\theta\approx-67.38^\circ`

We are not done here, however, as we need to account for which quadrant the vector is located in. Since v=⟨-5, 12⟩ is located in Quadrant II, then the direction angle must also be in Quadrant II.

Therefore, we use the formula
`\theta=180+\alpha` to account for this:

`\theta=180^\circ+\alpha\\\theta=180^\circ+(-67.38^\circ)\\\theta=180^\circ-67.38^\circ\\\theta=112.62^\circ\\\theta\approx113^\circ`