Finite Math Examples

$r \sin (x - \frac{π}{4}) = 8$

Step 1

Divide each term in $r \sin (x - \frac{π}{4}) = 8$ by $\sin (x - \frac{π}{4})$ .

$\frac{r \sin (x - \frac{π}{4})}{\sin (x - \frac{π}{4})} = \frac{8}{\sin (x - \frac{π}{4})}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\sin (x - \frac{π}{4})$ .

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Step 2.1.1

Cancel the common factor.

$\frac{r \sin (x - \frac{π}{4})}{\sin (x - \frac{π}{4})} = \frac{8}{\sin (x - \frac{π}{4})}$

Step 2.1.2

Divide $r$ by $1$ .

$r = \frac{8}{\sin (x - \frac{π}{4})}$

Step 3

Simplify the right side.

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Step 3.1

Separate fractions.

$r = \frac{8}{1} \cdot \frac{1}{\sin (x - \frac{π}{4})}$

Step 3.2

Convert from $\frac{1}{\sin (x - \frac{π}{4})}$ to $\csc (x - \frac{π}{4})$ .

$r = \frac{8}{1} \csc (x - \frac{π}{4})$

Step 3.3

Divide $8$ by $1$ .

$r = 8 \csc (x - \frac{π}{4})$