Find the X and Y Intercepts y=3tan(x)

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Trigonometry

$y = 3 \tan (x)$

Find the x-intercepts.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 3 \tan (x)$

Solve the equation.

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Rewrite the equation as $3 \tan (x) = 0$ .

$3 \tan (x) = 0$

Divide each term by $3$ and simplify.

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Divide each term in $3 \tan (x) = 0$ by $3$ .

$\frac{3 \tan (x)}{3} = \frac{0}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 \tan (x)}{3} = \frac{0}{3}$

Divide $\tan (x)$ by $1$ .

$\tan (x) = \frac{0}{3}$

Divide $0$ by $3$ .

$\tan (x) = 0$

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

$x = \arctan (0)$

The exact value of $\arctan (0)$ is $0$ .

$x = 0$

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.

$x = π + 0$

Add $π$ and $0$ .

$x = π$

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

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

$\frac{π}{| b |}$

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

$\frac{π}{| 1 |}$

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

$\frac{π}{1}$

Divide $π$ by $1$ .

$π$

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

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

Consolidate the answers.

$x = π n$ , for any integer $n$

x-intercept(s) in point form.

x-intercept(s): $(π n, 0)$ , for any integer $n$

Find the y-intercepts.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 3 \tan (0)$

Solve the equation.

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Remove parentheses.

$y = 3 \tan (0)$

Simplify $3 \tan (0)$ .

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The exact value of $\tan (0)$ is $0$ .

$y = 3 \cdot 0$

Multiply $3$ by $0$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

List the intersections.

x-intercept(s): $(π n, 0)$ , for any integer $n$

y-intercept(s): $(0, 0)$

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