Trigonometry Examples

$5 y = 4 \tan (x + 1)$

Step 1

Rewrite the equation as $4 \tan (x + 1) = 5 y$ .

$4 \tan (x + 1) = 5 y$

Step 2

Divide each term in $4 \tan (x + 1) = 5 y$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 \tan (x + 1) = 5 y$ by $4$ .

$\frac{4 \tan (x + 1)}{4} = \frac{5 y}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 \tan (x + 1)}{4} = \frac{5 y}{4}$

Step 2.2.1.2

Divide $\tan (x + 1)$ by $1$ .

$\tan (x + 1) = \frac{5 y}{4}$

Step 3

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

$x + 1 = \arctan (\frac{5 y}{4})$

Step 4

Subtract $1$ from both sides of the equation.

$x = \arctan (\frac{5 y}{4}) - 1$