Trigonometry Examples

$\frac{7 {(\sqrt{3})}^{2} + 7^{2} - {(7)}^{2}}{2 {(\sqrt{3})}^{2} (7)}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

$\frac{7 {(3^{\frac{1}{2}})}^{2} + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.1.2

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

$\frac{7 \cdot 3^{\frac{1}{2} \cdot 2} + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.1.3

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

$\frac{7 \cdot 3^{\frac{2}{2}} + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$\frac{7 \cdot 3^{\frac{2}{2}} + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.1.4.2

Rewrite the expression.

$\frac{7 \cdot 3^{1} + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.1.5

Evaluate the exponent.

$\frac{7 \cdot 3 + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.2

Multiply $7$ by $3$ .

$\frac{21 + 7^{2} - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.3

Raise $7$ to the power of $2$ .

$\frac{21 + 49 - 7^{2}}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.4

Raise $7$ to the power of $2$ .

$\frac{21 + 49 - 1 \cdot 49}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.5

Multiply $- 1$ by $49$ .

$\frac{21 + 49 - 49}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.6

Add $21$ and $49$ .

$\frac{70 - 49}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 1.7

Subtract $49$ from $70$ .

$\frac{21}{2 {\sqrt{3}}^{2} \cdot 7}$

Step 2

Simplify terms.

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Step 2.1

Multiply $7$ by $2$ .

$\frac{21}{14 {\sqrt{3}}^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{21}{14 {(3^{\frac{1}{2}})}^{2}}$

Step 2.2.2

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

$\frac{21}{14 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 2.2.3

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

$\frac{21}{14 \cdot 3^{\frac{2}{2}}}$

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Cancel the common factor.

$\frac{21}{14 \cdot 3^{\frac{2}{2}}}$

Step 2.2.4.2

Rewrite the expression.

$\frac{21}{14 \cdot 3^{1}}$

Step 2.2.5

Evaluate the exponent.

$\frac{21}{14 \cdot 3}$

Step 2.3

Multiply $14$ by $3$ .

$\frac{21}{42}$

Step 2.4

Cancel the common factor of $21$ and $42$ .

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Step 2.4.1

Factor $21$ out of $21$ .

$\frac{21 (1)}{42}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $21$ out of $42$ .

$\frac{21 \cdot 1}{21 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$\frac{21 \cdot 1}{21 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$