Trigonometry Examples

$r = 7 - 6 \sin (x)$

Step 1

Rewrite the equation as $7 - 6 \sin (x) = r$ .

$7 - 6 \sin (x) = r$

Step 2

Subtract $7$ from both sides of the equation.

$- 6 \sin (x) = r - 7$

Step 3

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

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Step 3.1

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

$\frac{- 6 \sin (x)}{- 6} = \frac{r}{- 6} + \frac{- 7}{- 6}$

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.

$\frac{- 6 \sin (x)}{- 6} = \frac{r}{- 6} + \frac{- 7}{- 6}$

Step 3.2.1.2

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

$\sin (x) = \frac{r}{- 6} + \frac{- 7}{- 6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$\sin (x) = - \frac{r}{6} + \frac{- 7}{- 6}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$\sin (x) = - \frac{r}{6} + \frac{7}{6}$

Step 4

Take the inverse sine of both sides of the equation to extract $x$ from inside the sine.

$x = \arcsin (- \frac{r}{6} + \frac{7}{6})$