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

$\cos^{2} (\frac{2 π}{3})$

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.

${(- \cos (\frac{π}{3}))}^{2}$

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

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{1}{2}$ .

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

Apply the product rule to $\frac{1}{2}$ .

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

Raise $- 1$ to the power of $2$ .

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

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

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

One to any power is one.

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

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

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

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

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