Trigonometry Examples

$y = \sin (\arctan (2))$

Step 1

Multiply $\frac{2}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$y = \frac{2 \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 2

Raise $\sqrt{5}$ to the power of $1$ .

$y = \frac{2 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Step 3

Raise $\sqrt{5}$ to the power of $1$ .

$y = \frac{2 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Step 4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{2 \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 5

Add $1$ and $1$ .

$y = \frac{2 \sqrt{5}}{{\sqrt{5}}^{2}}$

Step 6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$y = \frac{2 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$y = \frac{2 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$y = \frac{2 \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$y = \frac{2 \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$y = \frac{2 \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$y = \frac{2 \sqrt{5}}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{2 \sqrt{5}}{5}$

Decimal Form:

$y = 0.89442719 \dots$