Trigonometry Examples

6 \sin (θ) + 7 = 0

$6 \sin (θ) + 7 = 0$

Step 1

Subtract

7

$7$ from both sides of the equation.

6 \sin (θ) = - 7

$6 \sin (θ) = - 7$

Step 2

Divide each term in

6 \sin (θ) = - 7

$6 \sin (θ) = - 7$ by

6

$6$ and simplify.

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Step 2.1

Divide each term in

6 \sin (θ) = - 7

$6 \sin (θ) = - 7$ by

6

$6$ .

\frac{6 \sin (θ)}{6} = \frac{- 7}{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

$6$ .

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Step 2.2.1.1

Cancel the common factor.

\frac{6 \sin (θ)}{6} = \frac{- 7}{6}

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

Step 2.2.1.2

Divide

\sin (θ)

$\sin (θ)$ by

1

$1$ .

\sin (θ) = \frac{- 7}{6}

$\sin (θ) = \frac{- 7}{6}$

\sin (θ) = \frac{- 7}{6}

$\sin (θ) = \frac{- 7}{6}$

\sin (θ) = \frac{- 7}{6}

$\sin (θ) = \frac{- 7}{6}$

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}

$\sin (θ) = - \frac{7}{6}$

\sin (θ) = - \frac{7}{6}

$\sin (θ) = - \frac{7}{6}$

\sin (θ) = - \frac{7}{6}

$\sin (θ) = - \frac{7}{6}$

Step 3

The range of sine is

- 1 \leq y \leq 1

$- 1 \leq y \leq 1$ . Since

- \frac{7}{6}

$- \frac{7}{6}$ does not fall in this range, there is no solution.

No solution

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$