Find the Exact Value cos(((4pi)/3)/2)

$\cos (\frac{\frac{4 π}{3}}{2})$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\cos (\frac{4 π}{3} \cdot \frac{1}{2})$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $4 π$ .

$\cos (\frac{2 (2 π)}{3} \cdot \frac{1}{2})$

Cancel the common factor.

$\cos (\frac{2 (2 π)}{3} \cdot \frac{1}{2})$

Rewrite the expression.

$\cos (\frac{2 π}{3})$

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.

$- \cos (\frac{π}{3})$

Step 4

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

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$

Find the Exact Value cos(((4pi)/3)/2)

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