Calculus Examples

$\sin (\arccos (\frac{10 x}{11}))$

Step 1

Set the argument in $\arccos (\frac{10 x}{11})$ greater than or equal to $- 1$ to find where the expression is defined.

$\frac{10 x}{11} \geq - 1$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Multiply both sides by $11$ .

$\frac{10 x}{11} \cdot 11 \geq - 1 \cdot 11$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Simplify the left side.

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 2.2.1.1.1

Cancel the common factor.

$\frac{10 x}{11} \cdot 11 \geq - 1 \cdot 11$

Step 2.2.1.1.2

Rewrite the expression.

$10 x \geq - 1 \cdot 11$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Multiply $- 1$ by $11$ .

$10 x \geq - 11$

Step 2.3

Divide each term in $10 x \geq - 11$ by $10$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $10 x \geq - 11$ by $10$ .

$\frac{10 x}{10} \geq \frac{- 11}{10}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{10 x}{10} \geq \frac{- 11}{10}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 11}{10}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Move the negative in front of the fraction.

$x \geq - \frac{11}{10}$

Step 3

Set the argument in $\arccos (\frac{10 x}{11})$ less than or equal to $1$ to find where the expression is defined.

$\frac{10 x}{11} \leq 1$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Multiply both sides by $11$ .

$\frac{10 x}{11} \cdot 11 \leq 1 \cdot 11$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

Simplify the left side.

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 4.2.1.1.1

Cancel the common factor.

$\frac{10 x}{11} \cdot 11 \leq 1 \cdot 11$

Step 4.2.1.1.2

Rewrite the expression.

$10 x \leq 1 \cdot 11$

Step 4.2.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.1

Multiply $11$ by $1$ .

$10 x \leq 11$

Step 4.3

Divide each term in $10 x \leq 11$ by $10$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $10 x \leq 11$ by $10$ .

$\frac{10 x}{10} \leq \frac{11}{10}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{10 x}{10} \leq \frac{11}{10}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{11}{10}$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- \frac{11}{10}, \frac{11}{10}]$

Set-Builder Notation:

${x | - \frac{11}{10} \leq x \leq \frac{11}{10}}$

Step 6