Trigonometry Examples

$\tan (e^{y}) = \sqrt{x}$

Step 1

Substitute $u$ for $e^{y}$ .

$\tan (u) = \sqrt{x}$

Step 2

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

$u = \arctan (\sqrt{x})$

Step 3

Substitute $e^{y}$ for $u$ and solve $e^{y} = \arctan (\sqrt{x})$

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Step 3.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{y}) = \ln (\arctan (\sqrt{x}))$

Step 3.2

Expand the left side.

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Step 3.2.1

Expand $\ln (e^{y})$ by moving $y$ outside the logarithm.

$y \ln (e) = \ln (\arctan (\sqrt{x}))$

Step 3.2.2

The natural logarithm of $e$ is $1$ .

$y \cdot 1 = \ln (\arctan (\sqrt{x}))$

Step 3.2.3

Multiply $y$ by $1$ .

$y = \ln (\arctan (\sqrt{x}))$