Calculus Examples

$18 \cos (\frac{π}{6}) + 9 \sin (2 (\frac{π}{6}))$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$18 \frac{\sqrt{3}}{2} + 9 \sin (2 (\frac{π}{6}))$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $18$ .

$2 (9) \frac{\sqrt{3}}{2} + 9 \sin (2 (\frac{π}{6}))$

Step 1.2.2

Cancel the common factor.

$2 \cdot 9 \frac{\sqrt{3}}{2} + 9 \sin (2 (\frac{π}{6}))$

Step 1.2.3

Rewrite the expression.

$9 \sqrt{3} + 9 \sin (2 (\frac{π}{6}))$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $6$ .

$9 \sqrt{3} + 9 \sin (2 \frac{π}{2 (3)})$

Step 1.3.2

Cancel the common factor.

$9 \sqrt{3} + 9 \sin (2 \frac{π}{2 \cdot 3})$

Step 1.3.3

Rewrite the expression.

$9 \sqrt{3} + 9 \sin (\frac{π}{3})$

Step 1.4

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$9 \sqrt{3} + 9 \frac{\sqrt{3}}{2}$

Step 1.5

Combine $9$ and $\frac{\sqrt{3}}{2}$ .

$9 \sqrt{3} + \frac{9 \sqrt{3}}{2}$

Step 2

To write $9 \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 \sqrt{3} \cdot \frac{2}{2} + \frac{9 \sqrt{3}}{2}$

Step 3

Combine fractions.

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Step 3.1

Combine $9 \sqrt{3}$ and $\frac{2}{2}$ .

$\frac{9 \sqrt{3} \cdot 2}{2} + \frac{9 \sqrt{3}}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{9 \sqrt{3} \cdot 2 + 9 \sqrt{3}}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $9$ .

$\frac{18 \sqrt{3} + 9 \sqrt{3}}{2}$

Step 4.2

Add $18 \sqrt{3}$ and $9 \sqrt{3}$ .

$\frac{27 \sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{27 \sqrt{3}}{2}$

Decimal Form:

$23.38268590 \dots$