Trigonometry Examples

$S (r + t) = r t$

Step 1

Simplify $S (r + t)$ .

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Step 1.1

Rewrite.

$0 + 0 + S (r + t) = r t$

Step 1.2

Simplify by adding zeros.

$S (r + t) = r t$

Step 1.3

Apply the distributive property.

$S r + S t = r t$

Step 2

Subtract $r t$ from both sides of the equation.

$S r + S t - r t = 0$

Step 3

Subtract $S t$ from both sides of the equation.

$S r - r t = - S t$

Step 4

Factor $r$ out of $S r - r t$ .

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Step 4.1

Factor $r$ out of $S r$ .

$r S - r t = - S t$

Step 4.2

Factor $r$ out of $- r t$ .

$r S + r (- 1 t) = - S t$

Step 4.3

Factor $r$ out of $r S + r (- 1 t)$ .

$r (S - 1 t) = - S t$

Step 5

Rewrite $- 1 t$ as $- t$ .

$r (S - t) = - S t$

Step 6

Divide each term in $r (S - t) = - S t$ by $S - t$ and simplify.

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Step 6.1

Divide each term in $r (S - t) = - S t$ by $S - t$ .

$\frac{r (S - t)}{S - t} = \frac{- S t}{S - t}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $S - t$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{r (S - t)}{S - t} = \frac{- S t}{S - t}$

Step 6.2.1.2

Divide $r$ by $1$ .

$r = \frac{- S t}{S - t}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$r = - \frac{S t}{S - t}$