Trigonometry Examples

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

Step 1

Rewrite the equation as $\sqrt{\tan (x)} = y$ .

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

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\tan (x)}}^{2} = y^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\tan (x)}$ as ${\tan (x)}^{\frac{1}{2}}$ .

${({\tan (x)}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({\tan (x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({\tan (x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${\tan (x)}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${\tan (x)}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$\tan^{1} (x) = y^{2}$

Step 3.2.1.2

Simplify.

$\tan (x) = y^{2}$

Step 4

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

$x = \arctan (y^{2})$