Trigonometry Examples

$17 \sin (x) - 9 = 11 \sin (x) + 9$

Step 1

Move all terms containing $\sin (x)$ to the left side of the equation.

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Step 1.1

Subtract $11 \sin (x)$ from both sides of the equation.

$17 \sin (x) - 9 - 11 \sin (x) = 9$

Step 1.2

Subtract $11 \sin (x)$ from $17 \sin (x)$ .

$6 \sin (x) - 9 = 9$

Step 2

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

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Step 2.1

Add $9$ to both sides of the equation.

$6 \sin (x) = 9 + 9$

Step 2.2

Add $9$ and $9$ .

$6 \sin (x) = 18$

Step 3

Divide each term in $6 \sin (x) = 18$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 \sin (x) = 18$ by $6$ .

$\frac{6 \sin (x)}{6} = \frac{18}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 \sin (x)}{6} = \frac{18}{6}$

Step 3.2.1.2

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

$\sin (x) = \frac{18}{6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $18$ by $6$ .

$\sin (x) = 3$

Step 4

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

No solution