Trigonometry Examples

$\sin (\arctan (\sqrt{3}))$

Step 1

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\sqrt{3}}{\sqrt{1 + {(3^{\frac{1}{2}})}^{2}}}$

Step 1.2

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

$\frac{\sqrt{3}}{\sqrt{1 + 3^{\frac{1}{2} \cdot 2}}}$

Step 1.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{3}}{\sqrt{1 + 3^{\frac{2}{2}}}}$

Step 1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.4.1

Cancel the common factor.

$\frac{\sqrt{3}}{\sqrt{1 + 3^{\frac{2}{2}}}}$

Step 1.4.2

Rewrite the expression.

$\frac{\sqrt{3}}{\sqrt{1 + 3^{1}}}$

Step 1.5

Evaluate the exponent.

$\frac{\sqrt{3}}{\sqrt{1 + 3}}$

Step 2

Add $1$ and $3$ .

$\frac{\sqrt{3}}{\sqrt{4}}$

Step 3

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{3}}{\sqrt{2^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$