Precalculus Examples

$\cos (θ) = \frac{9}{\sqrt{481}}$

Step 1

Subtract $\frac{9}{\sqrt{481}}$ from both sides of the equation.

$\cos (θ) - \frac{9}{\sqrt{481}} = 0$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $\frac{9}{\sqrt{481}}$ by $\frac{\sqrt{481}}{\sqrt{481}}$ .

$\cos (θ) - (\frac{9}{\sqrt{481}} \cdot \frac{\sqrt{481}}{\sqrt{481}}) = 0$

Step 2.2

Combine and simplify the denominator.

Tap for more steps...

Step 2.2.1

Multiply $\frac{9}{\sqrt{481}}$ by $\frac{\sqrt{481}}{\sqrt{481}}$ .

$\cos (θ) - \frac{9 \sqrt{481}}{\sqrt{481} \sqrt{481}} = 0$

Step 2.2.2

Raise $\sqrt{481}$ to the power of $1$ .

$\cos (θ) - \frac{9 \sqrt{481}}{{\sqrt{481}}^{1} \sqrt{481}} = 0$

Step 2.2.3

Raise $\sqrt{481}$ to the power of $1$ .

$\cos (θ) - \frac{9 \sqrt{481}}{{\sqrt{481}}^{1} {\sqrt{481}}^{1}} = 0$

Step 2.2.4

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

$\cos (θ) - \frac{9 \sqrt{481}}{{\sqrt{481}}^{1 + 1}} = 0$

Step 2.2.5

Add $1$ and $1$ .

$\cos (θ) - \frac{9 \sqrt{481}}{{\sqrt{481}}^{2}} = 0$

Step 2.2.6

Rewrite ${\sqrt{481}}^{2}$ as $481$ .

Tap for more steps...

Step 2.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{481}$ as $481^{\frac{1}{2}}$ .

$\cos (θ) - \frac{9 \sqrt{481}}{{(481^{\frac{1}{2}})}^{2}} = 0$

Step 2.2.6.2

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

$\cos (θ) - \frac{9 \sqrt{481}}{481^{\frac{1}{2} \cdot 2}} = 0$

Step 2.2.6.3

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

$\cos (θ) - \frac{9 \sqrt{481}}{481^{\frac{2}{2}}} = 0$

Step 2.2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.6.4.1

Cancel the common factor.

$\cos (θ) - \frac{9 \sqrt{481}}{481^{\frac{2}{2}}} = 0$

Step 2.2.6.4.2

Rewrite the expression.

$\cos (θ) - \frac{9 \sqrt{481}}{481^{1}} = 0$

Step 2.2.6.5

Evaluate the exponent.

$\cos (θ) - \frac{9 \sqrt{481}}{481} = 0$

Step 3

The degree cannot be determined because $\cos (θ) - \frac{9 \sqrt{481}}{481}$ is not a polynomial.

Not a polynomial