Find the Tangent Given the Point (3/4,( square root of 7)/4)

$(\frac{3}{4}, \frac{\sqrt{7}}{4})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{3}{4}, \frac{\sqrt{7}}{4})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{3}{4}, 0)$ , and $(\frac{3}{4}, \frac{\sqrt{7}}{4})$ .

Opposite : $\frac{\sqrt{7}}{4}$

Adjacent : $\frac{3}{4}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{\sqrt{7}}{4}}{\frac{3}{4}}$ .

$\frac{\frac{\sqrt{7}}{4}}{\frac{3}{4}}$

Step 3

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{\sqrt{7}}{4} \cdot \frac{4}{3}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\tan (θ) = \frac{\sqrt{7}}{4} \cdot \frac{4}{3}$

Rewrite the expression.

$\tan (θ) = \sqrt{7} (\frac{1}{3})$

Combine $\sqrt{7}$ and $\frac{1}{3}$ .

$\tan (θ) = \frac{\sqrt{7}}{3}$

Step 4

Approximate the result.

$\tan (θ) = \frac{\sqrt{7}}{3} \approx 0.8819171$

Find the Tangent Given the Point (3/4,( square root of 7)/4)

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