Trigonometry Examples

$2 {(\frac{4}{\sqrt{17}})}^{2} - 1$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{4}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$2 {(\frac{4}{\sqrt{17}} \cdot \frac{\sqrt{17}}{\sqrt{17}})}^{2} - 1$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{4}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$2 {(\frac{4 \sqrt{17}}{\sqrt{17} \sqrt{17}})}^{2} - 1$

Step 1.2.2

Raise $\sqrt{17}$ to the power of $1$ .

$2 {(\frac{4 \sqrt{17}}{{\sqrt{17}}^{1} \sqrt{17}})}^{2} - 1$

Step 1.2.3

Raise $\sqrt{17}$ to the power of $1$ .

$2 {(\frac{4 \sqrt{17}}{{\sqrt{17}}^{1} {\sqrt{17}}^{1}})}^{2} - 1$

Step 1.2.4

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

$2 {(\frac{4 \sqrt{17}}{{\sqrt{17}}^{1 + 1}})}^{2} - 1$

Step 1.2.5

Add $1$ and $1$ .

$2 {(\frac{4 \sqrt{17}}{{\sqrt{17}}^{2}})}^{2} - 1$

Step 1.2.6

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$2 {(\frac{4 \sqrt{17}}{{(17^{\frac{1}{2}})}^{2}})}^{2} - 1$

Step 1.2.6.2

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

$2 {(\frac{4 \sqrt{17}}{17^{\frac{1}{2} \cdot 2}})}^{2} - 1$

Step 1.2.6.3

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

$2 {(\frac{4 \sqrt{17}}{17^{\frac{2}{2}}})}^{2} - 1$

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

$2 {(\frac{4 \sqrt{17}}{17^{\frac{2}{2}}})}^{2} - 1$

Step 1.2.6.4.2

Rewrite the expression.

$2 {(\frac{4 \sqrt{17}}{17^{1}})}^{2} - 1$

Step 1.2.6.5

Evaluate the exponent.

$2 {(\frac{4 \sqrt{17}}{17})}^{2} - 1$

Step 1.3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.3.1

Apply the product rule to $\frac{4 \sqrt{17}}{17}$ .

$2 \frac{{(4 \sqrt{17})}^{2}}{17^{2}} - 1$

Step 1.3.2

Apply the product rule to $4 \sqrt{17}$ .

$2 \frac{4^{2} {\sqrt{17}}^{2}}{17^{2}} - 1$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Raise $4$ to the power of $2$ .

$2 \frac{16 {\sqrt{17}}^{2}}{17^{2}} - 1$

Step 1.4.2

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 1.4.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$2 \frac{16 {(17^{\frac{1}{2}})}^{2}}{17^{2}} - 1$

Step 1.4.2.2

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

$2 \frac{16 \cdot 17^{\frac{1}{2} \cdot 2}}{17^{2}} - 1$

Step 1.4.2.3

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

$2 \frac{16 \cdot 17^{\frac{2}{2}}}{17^{2}} - 1$

Step 1.4.2.4

Cancel the common factor of $2$ .

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Step 1.4.2.4.1

Cancel the common factor.

$2 \frac{16 \cdot 17^{\frac{2}{2}}}{17^{2}} - 1$

Step 1.4.2.4.2

Rewrite the expression.

$2 \frac{16 \cdot 17^{1}}{17^{2}} - 1$

Step 1.4.2.5

Evaluate the exponent.

$2 \frac{16 \cdot 17}{17^{2}} - 1$

Step 1.5

Raise $17$ to the power of $2$ .

$2 \frac{16 \cdot 17}{289} - 1$

Step 1.6

Multiply $16$ by $17$ .

$2 (\frac{272}{289}) - 1$

Step 1.7

Cancel the common factor of $272$ and $289$ .

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Step 1.7.1

Factor $17$ out of $272$ .

$2 \frac{17 (16)}{289} - 1$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $17$ out of $289$ .

$2 \frac{17 \cdot 16}{17 \cdot 17} - 1$

Step 1.7.2.2

Cancel the common factor.

$2 \frac{17 \cdot 16}{17 \cdot 17} - 1$

Step 1.7.2.3

Rewrite the expression.

$2 (\frac{16}{17}) - 1$

Step 1.8

Multiply $2 (\frac{16}{17})$ .

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Step 1.8.1

Combine $2$ and $\frac{16}{17}$ .

$\frac{2 \cdot 16}{17} - 1$

Step 1.8.2

Multiply $2$ by $16$ .

$\frac{32}{17} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$\frac{32}{17} - 1 \cdot \frac{17}{17}$

Step 3

Combine $- 1$ and $\frac{17}{17}$ .

$\frac{32}{17} + \frac{- 1 \cdot 17}{17}$

Step 4

Combine the numerators over the common denominator.

$\frac{32 - 1 \cdot 17}{17}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $17$ .

$\frac{32 - 17}{17}$

Step 5.2

Subtract $17$ from $32$ .

$\frac{15}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{17}$

Decimal Form:

$0.88235294 \dots$