Trigonometry Examples

$\sin (2 \arcsin (7 x))$

Step 1

Set the argument in $\arcsin (7 x)$ less than $- 1$ to find where the expression is undefined.

$7 x < - 1$

Step 2

Divide each term in $7 x < - 1$ by $7$ and simplify.

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Step 2.1

Divide each term in $7 x < - 1$ by $7$ .

$\frac{7 x}{7} < \frac{- 1}{7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} < \frac{- 1}{7}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 1}{7}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$x < - \frac{1}{7}$

Step 3

Set the argument in $\arcsin (7 x)$ greater than $1$ to find where the expression is undefined.

$7 x > 1$

Step 4

Divide each term in $7 x > 1$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 x > 1$ by $7$ .

$\frac{7 x}{7} > \frac{1}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} > \frac{1}{7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{7}$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x < - \frac{1}{7}, x > \frac{1}{7}$

$(- \infty, - \frac{1}{7}) \cup (\frac{1}{7}, \infty)$

Step 6