Calculus Examples

$1 + 5 \cos (\frac{π}{3}) + \sec^{2} (\frac{π}{3})$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$1 + 5 (\frac{1}{2}) + \sec^{2} (\frac{π}{3})$

Step 1.2

Combine $5$ and $\frac{1}{2}$ .

$1 + \frac{5}{2} + \sec^{2} (\frac{π}{3})$

Step 1.3

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

$1 + \frac{5}{2} + 2^{2}$

Step 1.4

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

$1 + \frac{5}{2} + 4$

Step 2

Find the common denominator.

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Step 2.1

Write $1$ as a fraction with denominator $1$ .

$\frac{1}{1} + \frac{5}{2} + 4$

Step 2.2

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{1} \cdot \frac{2}{2} + \frac{5}{2} + 4$

Step 2.3

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{5}{2} + 4$

Step 2.4

Write $4$ as a fraction with denominator $1$ .

$\frac{2}{2} + \frac{5}{2} + \frac{4}{1}$

Step 2.5

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{5}{2} + \frac{4}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{5}{2} + \frac{4 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 5 + 4 \cdot 2}{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $4$ by $2$ .

$\frac{2 + 5 + 8}{2}$

Step 4.2

Add $2$ and $5$ .

$\frac{7 + 8}{2}$

Step 4.3

Add $7$ and $8$ .

$\frac{15}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$