Trigonometry Examples

$v (\frac{2 \cdot 90}{32 \cdot (\frac{\sqrt{3}}{2}) \cdot (\frac{1}{2})})$

Step 1

Multiply $2$ by $90$ .

$v \frac{180}{32 \cdot (\frac{\sqrt{3}}{2}) \cdot (\frac{1}{2})}$

Step 2

Simplify the denominator.

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Step 2.1

Combine $32$ and $\frac{\sqrt{3}}{2}$ .

$v \frac{180}{\frac{32 \sqrt{3}}{2} \cdot \frac{1}{2}}$

Step 2.2

Multiply $\frac{32 \sqrt{3}}{2}$ by $\frac{1}{2}$ .

$v \frac{180}{\frac{32 \sqrt{3}}{2 \cdot 2}}$

Step 3

Multiply $2$ by $2$ .

$v \frac{180}{\frac{32 \sqrt{3}}{4}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{32 \sqrt{3}}{4}$ by cancelling the common factors.

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Step 4.1.1

Factor $4$ out of $32 \sqrt{3}$ .

$v \frac{180}{\frac{4 (8 \sqrt{3})}{4}}$

Step 4.1.2

Factor $4$ out of $4$ .

$v \frac{180}{\frac{4 (8 \sqrt{3})}{4 (1)}}$

Step 4.1.3

Cancel the common factor.

$v \frac{180}{\frac{4 (8 \sqrt{3})}{4 \cdot 1}}$

Step 4.1.4

Rewrite the expression.

$v \frac{180}{\frac{8 \sqrt{3}}{1}}$

Step 4.2

Divide $8 \sqrt{3}$ by $1$ .

$v \frac{180}{8 \sqrt{3}}$

Step 5

Cancel the common factor of $180$ and $8$ .

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Step 5.1

Factor $4$ out of $180$ .

$v \frac{4 (45)}{8 \sqrt{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $4$ out of $8 \sqrt{3}$ .

$v \frac{4 (45)}{4 (2 \sqrt{3})}$

Step 5.2.2

Cancel the common factor.

$v \frac{4 \cdot 45}{4 (2 \sqrt{3})}$

Step 5.2.3

Rewrite the expression.

$v \frac{45}{2 \sqrt{3}}$

Step 6

Multiply $\frac{45}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$v (\frac{45}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{45}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$v \frac{45 \sqrt{3}}{2 \sqrt{3} \sqrt{3}}$

Step 7.2

Move $\sqrt{3}$ .

$v \frac{45 \sqrt{3}}{2 (\sqrt{3} \sqrt{3})}$

Step 7.3

Raise $\sqrt{3}$ to the power of $1$ .

$v \frac{45 \sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 7.4

Raise $\sqrt{3}$ to the power of $1$ .

$v \frac{45 \sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 7.5

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

$v \frac{45 \sqrt{3}}{2 {\sqrt{3}}^{1 + 1}}$

Step 7.6

Add $1$ and $1$ .

$v \frac{45 \sqrt{3}}{2 {\sqrt{3}}^{2}}$

Step 7.7

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

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Step 7.7.1

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

$v \frac{45 \sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}}$

Step 7.7.2

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

$v \frac{45 \sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 7.7.3

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

$v \frac{45 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Step 7.7.4

Cancel the common factor of $2$ .

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Step 7.7.4.1

Cancel the common factor.

$v \frac{45 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Step 7.7.4.2

Rewrite the expression.

$v \frac{45 \sqrt{3}}{2 \cdot 3^{1}}$

Step 7.7.5

Evaluate the exponent.

$v \frac{45 \sqrt{3}}{2 \cdot 3}$

Step 8

Multiply $2$ by $3$ .

$v \frac{45 \sqrt{3}}{6}$

Step 9

Cancel the common factor of $45$ and $6$ .

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Step 9.1

Factor $3$ out of $45 \sqrt{3}$ .

$v \frac{3 (15 \sqrt{3})}{6}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $6$ .

$v \frac{3 (15 \sqrt{3})}{3 (2)}$

Step 9.2.2

Cancel the common factor.

$v \frac{3 (15 \sqrt{3})}{3 \cdot 2}$

Step 9.2.3

Rewrite the expression.

$v \frac{15 \sqrt{3}}{2}$

Step 10

Combine $v$ and $\frac{15 \sqrt{3}}{2}$ .

$\frac{v (15 \sqrt{3})}{2}$

Step 11

Move $15$ to the left of $v$ .

$\frac{15 v \sqrt{3}}{2}$