Precalculus Examples

$\tan (x) = \frac{875}{350}$

Step 1

Subtract $\frac{875}{350}$ from both sides of the equation.

$\tan (x) - \frac{875}{350} = 0$

Step 2

Cancel the common factor of $875$ and $350$ .

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Step 2.1

Factor $175$ out of $875$ .

$\tan (x) - \frac{175 (5)}{350} = 0$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $175$ out of $350$ .

$\tan (x) - \frac{175 \cdot 5}{175 \cdot 2} = 0$

Step 2.2.2

Cancel the common factor.

$\tan (x) - \frac{175 \cdot 5}{175 \cdot 2} = 0$

Step 2.2.3

Rewrite the expression.

$\tan (x) - \frac{5}{2} = 0$

Step 3

Add $\frac{5}{2}$ to both sides of the equation.

$\tan (x) = \frac{5}{2}$

Step 4

Take the inverse tangent of both sides of the equation to extract $x$ from inside the tangent.

$x = \arctan (\frac{5}{2})$

Step 5

Simplify the right side.

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Step 5.1

Evaluate $\arctan (\frac{5}{2})$ .

$x = 1.19028994$

Step 6

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from $π$ to find the solution in the fourth quadrant.

$x = (3.14159265) + 1.19028994$

Step 7

Solve for $x$ .

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Step 7.1

Remove parentheses.

$x = 3.14159265 + 1.19028994$

Step 7.2

Remove parentheses.

$x = (3.14159265) + 1.19028994$

Step 7.3

Add $3.14159265$ and $1.19028994$ .

$x = 4.3318826$

Step 8

Find the period of $\tan (x)$ .

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Step 8.1

The period of the function can be calculated using $\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Step 8.2

Replace $b$ with $1$ in the formula for period.

$\frac{π}{| 1 |}$

Step 8.3

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{π}{1}$

Step 8.4

Divide $π$ by $1$ .

$π$

Step 9

The period of the $\tan (x)$ function is $π$ so values will repeat every $π$ radians in both directions.

$x = 1.19028994 + π n, 4.3318826 + π n$ , for any integer $n$

Step 10

Consolidate $1.19028994 + π n$ and $4.3318826 + π n$ to $1.19028994 + π n$ .

$x = 1.19028994 + π n$ , for any integer $n$