Trigonometry Examples

$y = a \sin (k (x - b))$

Step 1

Rewrite the equation as $a \sin (k (x - b)) = y$ .

$a \sin (k (x - b)) = y$

Step 2

Divide each term in $a \sin (k (x - b)) = y$ by $\sin (k (x - b))$ and simplify.

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Step 2.1

Divide each term in $a \sin (k (x - b)) = y$ by $\sin (k (x - b))$ .

$\frac{a \sin (k (x - b))}{\sin (k (x - b))} = \frac{y}{\sin (k (x - b))}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sin (k (x - b))$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a \sin (k (x - b))}{\sin (k (x - b))} = \frac{y}{\sin (k (x - b))}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{y}{\sin (k (x - b))}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Separate fractions.

$a = \frac{y}{1} \cdot \frac{1}{\sin (k (x - b))}$

Step 2.3.2

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

$a = \frac{y}{1} \csc (k (x - b))$

Step 2.3.3

Divide $y$ by $1$ .

$a = y \csc (k (x - b))$

Step 2.3.4

Apply the distributive property.

$a = y \csc (k x + k (- b))$

Step 2.3.5

Rewrite using the commutative property of multiplication.

$a = y \csc (k x - k b)$