Trigonometry Examples

$x = \tan (\frac{1}{4} - \frac{3}{4})$

Step 1

Simplify $\tan (\frac{1}{4} - \frac{3}{4})$ .

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Step 1.1

Combine the numerators over the common denominator.

$x = \tan (\frac{1 - 3}{4})$

Step 1.2

Subtract $3$ from $1$ .

$x = \tan (\frac{- 2}{4})$

Step 1.3

Cancel the common factor of $- 2$ and $4$ .

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Step 1.3.1

Factor $2$ out of $- 2$ .

$x = \tan (\frac{2 (- 1)}{4})$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $4$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 1.4

Move the negative in front of the fraction.

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

Step 1.5

Evaluate $\tan (- \frac{1}{2})$ .

$x = - 0.54630248$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.54630248$

Step 3