Trigonometry Examples

$\cos (\arctan (- \frac{5}{8}))$

Step 1

Multiply $\frac{8}{\sqrt{89}}$ by $\frac{\sqrt{89}}{\sqrt{89}}$ .

$\frac{8 \sqrt{89}}{\sqrt{89} \sqrt{89}}$

Step 2

Raise $\sqrt{89}$ to the power of $1$ .

$\frac{8 \sqrt{89}}{{\sqrt{89}}^{1} \sqrt{89}}$

Step 3

Raise $\sqrt{89}$ to the power of $1$ .

$\frac{8 \sqrt{89}}{{\sqrt{89}}^{1} {\sqrt{89}}^{1}}$

Step 4

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

$\frac{8 \sqrt{89}}{{\sqrt{89}}^{1 + 1}}$

Step 5

Add $1$ and $1$ .

$\frac{8 \sqrt{89}}{{\sqrt{89}}^{2}}$

Step 6

Rewrite ${\sqrt{89}}^{2}$ as $89$ .

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{89}$ as $89^{\frac{1}{2}}$ .

$\frac{8 \sqrt{89}}{{(89^{\frac{1}{2}})}^{2}}$

Step 6.2

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

$\frac{8 \sqrt{89}}{89^{\frac{1}{2} \cdot 2}}$

Step 6.3

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

$\frac{8 \sqrt{89}}{89^{\frac{2}{2}}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$\frac{8 \sqrt{89}}{89^{\frac{2}{2}}}$

Step 6.4.2

Rewrite the expression.

$\frac{8 \sqrt{89}}{89^{1}}$

Step 6.5

Evaluate the exponent.

$\frac{8 \sqrt{89}}{89}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{89}}{89}$

Decimal Form:

$0.84799830 \dots$