Evaluate Using the Given Value

$\cos (\frac{x}{2})$ , $x = 2 π$

Step 1

Replace the variable $x$ with $2 π$ in the expression.

$\cos (\frac{2 π}{2})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\cos (\frac{2 π}{2})$

Step 2.2

Divide $π$ by $1$ .

$\cos (π)$

Step 3

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.

$- \cos (0)$

Step 4

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

$- 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$- 1$

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Simplifying and Evaluating Expressions

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Simplifying Multiplication Polynomial Addition Polynomial Subtraction Polynomial Multiplication Polynomial Division Simplifying Expressions Multiplying Polynomials Using FOIL Identifying Degree Operations on Polynomials Negative Exponents Evaluating Radicals

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$