Trigonometry Examples

$(- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{1}{\sqrt{2}}, 0)$ , and $(- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$ .

Opposite : $- \frac{1}{\sqrt{2}}$

Adjacent : $- \frac{1}{\sqrt{2}}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- \frac{1}{\sqrt{2}}}{- \frac{1}{\sqrt{2}}}$ .

$\frac{- \frac{1}{\sqrt{2}}}{- \frac{1}{\sqrt{2}}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Dividing two negative values results in a positive value.

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

Step 3.2

Cancel the common factor of $\frac{1}{\sqrt{2}}$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\tan (θ) = 1$