Trigonometry Examples

$(- 3 π, \frac{3 π}{2})$

Step 1

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

Opposite : $\frac{3 π}{2}$

Adjacent : $- 3 π$

Step 2

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

$\frac{\frac{3 π}{2}}{- 3 π}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Cancel the common factor of $3 π$ .

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Step 3.2.1

Factor $3 π$ out of $- 3 π$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.3

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

$\tan (θ) = \frac{1}{2 \cdot - 1}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $2$ by $- 1$ .

$\tan (θ) = \frac{1}{- 2}$

Step 3.4.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{1}{2}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{1}{2} \approx - 0.5$