Trigonometry Examples

$\sin (3 x) - 1 = \frac{1}{2}$

Step 1

Move all terms not containing $\sin (3 x)$ to the right side of the equation.

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Step 1.1

Add $1$ to both sides of the equation.

$\sin (3 x) = \frac{1}{2} + 1$

Step 1.2

Write $1$ as a fraction with a common denominator.

$\sin (3 x) = \frac{1}{2} + \frac{2}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\sin (3 x) = \frac{1 + 2}{2}$

Step 1.4

Add $1$ and $2$ .

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

Step 2

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