Trigonometry Examples

$6 \sin (θ) + 7 = 0$

Step 1

Subtract $7$ from both sides of the equation.

$6 \sin (θ) = - 7$

Step 2

Divide each term in $6 \sin (θ) = - 7$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 \sin (θ) = - 7$ by $6$ .

$\frac{6 \sin (θ)}{6} = \frac{- 7}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 \sin (θ)}{6} = \frac{- 7}{6}$

Step 2.2.1.2

Divide $\sin (θ)$ by $1$ .

$\sin (θ) = \frac{- 7}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\sin (θ) = - \frac{7}{6}$

Step 3

The range of sine is $- 1 \leq y \leq 1$ . Since $- \frac{7}{6}$ does not fall in this range, there is no solution.

No solution