Precalculus Examples

$- 6 i + 2 j$

Step 1

Apply the direction angle formula $θ = \arctan (\frac{b}{a})$ where $a = - 6$ and $b = 2$ .

$θ = \arctan (\frac{2}{- 6})$

Step 2

Solve for $θ$ .

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Step 2.1

Remove parentheses.

$θ = \arctan (\frac{2}{- 6})$

Step 2.2

Simplify $\arctan (\frac{2}{- 6})$ .

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Step 2.2.1

Cancel the common factor of $2$ and $- 6$ .

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Step 2.2.1.1

Factor $2$ out of $2$ .

$θ = \arctan (\frac{2 (1)}{- 6})$

Step 2.2.1.2

Cancel the common factors.

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Step 2.2.1.2.1

Factor $2$ out of $- 6$ .

$θ = \arctan (\frac{2 \cdot 1}{2 \cdot - 3})$

Step 2.2.1.2.2

Cancel the common factor.

$θ = \arctan (\frac{2 \cdot 1}{2 \cdot - 3})$

Step 2.2.1.2.3

Rewrite the expression.

$θ = \arctan (\frac{1}{- 3})$

Step 2.2.2

Move the negative in front of the fraction.

$θ = \arctan (- \frac{1}{3})$

Step 2.2.3

Evaluate $\arctan (- \frac{1}{3})$ .

$θ = - 0.32175055$