Precalculus Examples

$2 \sin (2 x) - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$2 \sin (2 x) = 3$

Step 2

Divide each term in $2 \sin (2 x) = 3$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 \sin (2 x) = 3$ by $2$ .

$\frac{2 \sin (2 x)}{2} = \frac{3}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 \sin (2 x)}{2} = \frac{3}{2}$

Step 2.2.1.2

Divide $\sin (2 x)$ by $1$ .

$\sin (2 x) = \frac{3}{2}$

Step 3

The range of sine is $- 1 \leq y \leq 1$ . Since $\frac{3}{2}$ does not fall in this range, there is no solution.

No solution