Trigonometry Examples

$y = 3 \cos (x - π) - 4$

Step 1

Rewrite the equation as $3 \cos (x - π) - 4 = y$ .

$3 \cos (x - π) - 4 = y$

Step 2

Add $4$ to both sides of the equation.

$3 \cos (x - π) = y + 4$

Step 3

Divide each term in $3 \cos (x - π) = y + 4$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 \cos (x - π) = y + 4$ by $3$ .

$\frac{3 \cos (x - π)}{3} = \frac{y}{3} + \frac{4}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 \cos (x - π)}{3} = \frac{y}{3} + \frac{4}{3}$

Step 3.2.1.2

Divide $\cos (x - π)$ by $1$ .

$\cos (x - π) = \frac{y}{3} + \frac{4}{3}$

Step 4

Take the inverse cosine of both sides of the equation to extract $x$ from inside the cosine.

$x - π = \arccos (\frac{y}{3} + \frac{4}{3})$

Step 5

Add $π$ to both sides of the equation.

$x = \arccos (\frac{y}{3} + \frac{4}{3}) + π$