Trigonometry Examples

$y = A \tan (B x - c)$

Step 1

Rewrite the equation as $A \tan (B x - c) = y$ .

$A \tan (B x - c) = y$

Step 2

Divide each term in $A \tan (B x - c) = y$ by $\tan (B x - c)$ and simplify.

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Step 2.1

Divide each term in $A \tan (B x - c) = y$ by $\tan (B x - c)$ .

$\frac{A \tan (B x - c)}{\tan (B x - c)} = \frac{y}{\tan (B x - c)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\tan (B x - c)$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \tan (B x - c)}{\tan (B x - c)} = \frac{y}{\tan (B x - c)}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{y}{\tan (B x - c)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Separate fractions.

$A = \frac{y}{1} \cdot \frac{1}{\tan (B x - c)}$

Step 2.3.2

Rewrite $\tan (B x - c)$ in terms of sines and cosines.

$A = \frac{y}{1} \cdot \frac{1}{\frac{\sin (B x - c)}{\cos (B x - c)}}$

Step 2.3.3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (B x - c)}{\cos (B x - c)}$ .

$A = \frac{y}{1} \cdot \frac{\cos (B x - c)}{\sin (B x - c)}$

Step 2.3.4

Convert from $\frac{\cos (B x - c)}{\sin (B x - c)}$ to $\cot (B x - c)$ .

$A = \frac{y}{1} \cot (B x - c)$

Step 2.3.5

Divide $y$ by $1$ .

$A = y \cot (B x - c)$