Trigonometry Examples

$(3, \frac{7 π}{2})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(3, \frac{7 π}{2})$ , draw the triangle between the three points $(0, 0)$ , $(3, 0)$ , and $(3, \frac{7 π}{2})$ .

Opposite : $\frac{7 π}{2}$

Adjacent : $3$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{7 π}{2}}{3}$ .

$\frac{\frac{7 π}{2}}{3}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{7 π}{2} \cdot \frac{1}{3}$

Step 3.2

Multiply $\frac{7 π}{2} \cdot \frac{1}{3}$ .

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Step 3.2.1

Multiply $\frac{7 π}{2}$ by $\frac{1}{3}$ .

$\tan (θ) = \frac{7 π}{2 \cdot 3}$

Step 3.2.2

Multiply $2$ by $3$ .

$\tan (θ) = \frac{7 π}{6}$

Step 4

Approximate the result.

$\tan (θ) = \frac{7 π}{6} \approx 3.66519142$