Graph y=arcsin(2x)

$y = \arcsin (2 x)$

Step 1

Select a few points to graph.

Find the point at $x = - \frac{1}{2}$ .

Replace the variable $x$ with $- \frac{1}{2}$ in the expression.

$f (- \frac{1}{2}) = \arcsin (2 (- \frac{1}{2}))$

Simplify the result.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$f (- \frac{1}{2}) = \arcsin (2 (\frac{- 1}{2}))$

Cancel the common factor.

$f (- \frac{1}{2}) = \arcsin (2 (\frac{- 1}{2}))$

Rewrite the expression.

$f (- \frac{1}{2}) = \arcsin (- 1)$

The exact value of $\arcsin (- 1)$ is $- \frac{π}{2}$ .

$f (- \frac{1}{2}) = - \frac{π}{2}$

The final answer is $- \frac{π}{2}$ .

$- \frac{π}{2}$

Find the point at $x = - \frac{1}{4}$ .

Replace the variable $x$ with $- \frac{1}{4}$ in the expression.

$f (- \frac{1}{4}) = \arcsin (2 (- \frac{1}{4}))$

Simplify the result.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$f (- \frac{1}{4}) = \arcsin (2 (\frac{- 1}{4}))$

Factor $2$ out of $4$ .

$f (- \frac{1}{4}) = \arcsin (2 (\frac{- 1}{2 (2)}))$

Cancel the common factor.

$f (- \frac{1}{4}) = \arcsin (2 (\frac{- 1}{2 \cdot 2}))$

Rewrite the expression.

$f (- \frac{1}{4}) = \arcsin (\frac{- 1}{2})$

Move the negative in front of the fraction.

$f (- \frac{1}{4}) = \arcsin (- \frac{1}{2})$

The exact value of $\arcsin (- \frac{1}{2})$ is $- \frac{π}{6}$ .

$f (- \frac{1}{4}) = - \frac{π}{6}$

The final answer is $- \frac{π}{6}$ .

$- \frac{π}{6}$

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = \arcsin (2 (0))$

Simplify the result.

Multiply $2$ by $0$ .

$f (0) = \arcsin (0)$

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

$f (0) = 0$

The final answer is $0$ .

$0$

Find the point at $x = \frac{1}{4}$ .

Replace the variable $x$ with $\frac{1}{4}$ in the expression.

$f (\frac{1}{4}) = \arcsin (2 (\frac{1}{4}))$

Simplify the result.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$f (\frac{1}{4}) = \arcsin (2 (\frac{1}{2 (2)}))$

Cancel the common factor.

$f (\frac{1}{4}) = \arcsin (2 (\frac{1}{2 \cdot 2}))$

Rewrite the expression.

$f (\frac{1}{4}) = \arcsin (\frac{1}{2})$

The exact value of $\arcsin (\frac{1}{2})$ is $\frac{π}{6}$ .

$f (\frac{1}{4}) = \frac{π}{6}$

The final answer is $\frac{π}{6}$ .

$\frac{π}{6}$

Find the point at $x = \frac{1}{2}$ .

Replace the variable $x$ with $\frac{1}{2}$ in the expression.

$f (\frac{1}{2}) = \arcsin (2 (\frac{1}{2}))$

Simplify the result.

Cancel the common factor of $2$ .

Cancel the common factor.

$f (\frac{1}{2}) = \arcsin (2 (\frac{1}{2}))$

Rewrite the expression.

$f (\frac{1}{2}) = \arcsin (1)$

The exact value of $\arcsin (1)$ is $\frac{π}{2}$ .

$f (\frac{1}{2}) = \frac{π}{2}$

The final answer is $\frac{π}{2}$ .

$\frac{π}{2}$

List the points in a table.

$\begin{array}{c} x & f (x) \\ - \frac{1}{2} & - \frac{π}{2} \\ - \frac{1}{4} & - \frac{π}{6} \\ 0 & 0 \\ \frac{1}{4} & \frac{π}{6} \\ \frac{1}{2} & \frac{π}{2} \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - \frac{1}{2} & - \frac{π}{2} \\ - \frac{1}{4} & - \frac{π}{6} \\ 0 & 0 \\ \frac{1}{4} & \frac{π}{6} \\ \frac{1}{2} & \frac{π}{2} \end{array}$

Step 3

Graph y=arcsin(2x)

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