Trigonometry Examples

$y = A \cos (x + c)$

Step 1

Rewrite the equation as $A \cos (x + c) = y$ .

$A \cos (x + c) = y$

Step 2

Divide each term in $A \cos (x + c) = y$ by $\cos (x + c)$ and simplify.

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Step 2.1

Divide each term in $A \cos (x + c) = y$ by $\cos (x + c)$ .

$\frac{A \cos (x + c)}{\cos (x + c)} = \frac{y}{\cos (x + c)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\cos (x + c)$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \cos (x + c)}{\cos (x + c)} = \frac{y}{\cos (x + c)}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{y}{\cos (x + c)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Separate fractions.

$A = \frac{y}{1} \cdot \frac{1}{\cos (x + c)}$

Step 2.3.2

Convert from $\frac{1}{\cos (x + c)}$ to $\sec (x + c)$ .

$A = \frac{y}{1} \sec (x + c)$

Step 2.3.3

Divide $y$ by $1$ .

$A = y \sec (x + c)$