Trigonometry Examples

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

Step 1

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

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

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

Step 2

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

$\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\tan (θ) = 1$