Linear Algebra Examples

$(- 4, 0.5)$

Step 1

Apply the direction angle formula $θ = \arctan (\frac{b}{a})$ where $a = - 4$ and $b = 0.5$ .

$θ = \arctan (\frac{0.5}{- 4})$

Step 2

Solve for $θ$ .

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Step 2.1

Remove parentheses.

$θ = \arctan (\frac{0.5}{- 4})$

Step 2.2

Simplify $\arctan (\frac{0.5}{- 4})$ .

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Step 2.2.1

Divide $0.5$ by $- 4$ .

$θ = \arctan (- 0.125)$

Step 2.2.2

Evaluate $\arctan (- 0.125)$ .

$θ = - 7.12501634$

Step 3

Since the angle is in the second quadrant, add $180$ to $- 7.12501634$ .

$θ = - 7.12501634 + 180$

Step 4

Add $- 7.12501634$ and $180$ .

$θ = 172.87498365$

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