Precalculus Examples

$- 4 i - 8 j$

Step 1

Apply the direction angle formula $θ = \arctan (\frac{b}{a})$ where $a = - 4$ and $b = - 8$ .

$θ = \arctan (- \frac{8}{- 4})$

Step 2

Solve for $θ$ .

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Step 2.1

Remove parentheses.

$θ = \arctan (- \frac{8}{- 4})$

Step 2.2

Simplify $\arctan (- \frac{8}{- 4})$ .

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Step 2.2.1

Divide $8$ by $- 4$ .

$θ = \arctan (- - 2)$

Step 2.2.2

Multiply $- 1$ by $- 2$ .

$θ = \arctan (2)$

Step 2.2.3

Evaluate $\arctan (2)$ .

$θ = 1.10714871$