Graph y=tan(2x)

$y = \tan (2 x)$

Find the asymptotes.

Tap for more steps...

For any $y = \tan (x)$ , vertical asymptotes occur at $x = \frac{π}{2} + n π$ , where $n$ is an integer. Use the basic period for $y = \tan (x)$ , $(- \frac{π}{2}, \frac{π}{2})$ , to find the vertical asymptotes for $y = \tan (2 x)$ . Set the inside of the tangent function, $b x + c$ , for $y = a \tan (b x + c) + d$ equal to $- \frac{π}{2}$ to find where the vertical asymptote occurs for $y = \tan (2 x)$ .

$2 x = - \frac{π}{2}$

Divide each term by $2$ and simplify.

Tap for more steps...

Divide each term in $2 x = - \frac{π}{2}$ by $2$ .

$\frac{2 x}{2} = - \frac{π}{2} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 x}{2} = - \frac{π}{2} \cdot \frac{1}{2}$

Divide $x$ by $1$ .

$x = - \frac{π}{2} \cdot \frac{1}{2}$

Multiply $- \frac{π}{2} \cdot \frac{1}{2}$ .

Tap for more steps...

Multiply $\frac{1}{2}$ and $\frac{π}{2}$ .

$x = - \frac{π}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = - \frac{π}{4}$

Set the inside of the tangent function $2 x$ equal to $\frac{π}{2}$ .

$2 x = \frac{π}{2}$

Divide each term by $2$ and simplify.

Tap for more steps...

Divide each term in $2 x = \frac{π}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{π}{2} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 x}{2} = \frac{π}{2} \cdot \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{π}{2} \cdot \frac{1}{2}$

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

Tap for more steps...

Multiply $\frac{π}{2}$ and $\frac{1}{2}$ .

$x = \frac{π}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{π}{4}$

The basic period for $y = \tan (2 x)$ will occur at $(- \frac{π}{4}, \frac{π}{4})$ , where $- \frac{π}{4}$ and $\frac{π}{4}$ are vertical asymptotes.

$(- \frac{π}{4}, \frac{π}{4})$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{π}{2}$

The vertical asymptotes for $y = \tan (2 x)$ occur at $- \frac{π}{4}$ , $\frac{π}{4}$ , and every $\frac{π n}{2}$ , where $n$ is an integer.

$x = \frac{π}{4} + \frac{π n}{2}$

Tangent only has vertical asymptotes.

No Horizontal Asymptotes

No Oblique Asymptotes

Vertical Asymptotes: $x = \frac{π}{4} + \frac{π n}{2}$ where $n$ is an integer

No Horizontal Asymptotes

No Oblique Asymptotes

Vertical Asymptotes: $x = \frac{π}{4} + \frac{π n}{2}$ where $n$ is an integer

Use the form $a \tan (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = 1$

$b = 2$

$c = 0$

$d = 0$

Since the graph of the function $t a n$ does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

Find the period of $\tan (2 x)$ .

Tap for more steps...

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

$\frac{π}{| b |}$

Replace $b$ with $2$ in the formula for period.

$\frac{π}{| 2 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{π}{2}$

Find the phase shift using the formula $\frac{c}{b}$ .

Tap for more steps...

The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{0}{2}$

Divide $0$ by $2$ .

Phase Shift: $0$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{π}{2}$

Phase Shift: $0$ ( $0$ to the right)

Vertical Shift: $0$

The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.

Vertical Asymptotes: $x = \frac{π}{4} + \frac{π n}{2}$ where $n$ is an integer

Amplitude: None

Period: $\frac{π}{2}$

Phase Shift: $0$ ( $0$ to the right)

Vertical Shift: $0$

Do you know how to Graph y=tan(2x)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Find the Other Trig Values in Quadrant III sin(x)=-11/61

Factor sin(x+y)-sin(x-y)

Expand the Logarithmic Expression log base 6 of ((x^5)/y)^6

Determine if True cos((5pi)/3)=( square root of 2)/2

Determine if True (3pi)/4=- square root of 2/2