Finite Math Examples

$P = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$

Step 1

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

$θ = \arctan (\frac{\frac{\frac{\sqrt{2}}{2}}{\sqrt{2}}}{2})$

Step 2

Solve for $θ$ .

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Step 2.1

Remove parentheses.

$θ = \arctan (\frac{\frac{\frac{\sqrt{2}}{2}}{\sqrt{2}}}{2})$

Step 2.2

Simplify $\arctan (\frac{\frac{\frac{\sqrt{2}}{2}}{\sqrt{2}}}{2})$ .

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Step 2.2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2.3

Cancel the common factor of $\sqrt{2}$ .

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Step 2.2.3.1

Cancel the common factor.

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

Step 2.2.3.2

Rewrite the expression.

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

Step 2.2.4

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 2.2.4.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$θ = \arctan (\frac{1}{2 \cdot 2})$

Step 2.2.4.2

Multiply $2$ by $2$ .

$θ = \arctan (\frac{1}{4})$

Step 2.2.5

Evaluate $\arctan (\frac{1}{4})$ .

$θ = 14.03624346$