Calculus Examples

$\frac{\cos (2 π)}{2} - 2 \cos (π)$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{\cos (0)}{2} - 2 \cos (π)$

Step 1.1.2

The exact value of $\cos (0)$ is $1$ .

$\frac{1}{2} - 2 \cos (π)$

Step 1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$\frac{1}{2} - 2 (- \cos (0))$

Step 1.3

The exact value of $\cos (0)$ is $1$ .

$\frac{1}{2} - 2 (- 1 \cdot 1)$

Step 1.4

Multiply $- 2 (- 1 \cdot 1)$ .

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Step 1.4.1

Multiply $- 1$ by $1$ .

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

Step 1.4.2

Multiply $- 2$ by $- 1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

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

Step 5.2

Add $1$ and $4$ .

$\frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$