What is the value of cos^2(1/2*(2pi)/3) ?

The value of cos^2(1/2*(2pi)/3) is 1/4

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cos^2(1/2*(2pi)/3)

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Simplify:

\frac{1}{2} \cdot \frac{2 π}{3} = \frac{π}{3}

\frac{1}{2} \cdot \frac{2 π}{3}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 2 π}{2 \cdot 3}

Cancel the common factor:

2

= \frac{1 π}{3}

Multiply:

1 π = π

= \frac{π}{3}

= cos^{2} (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= (\frac{1}{2})^{2}

Simplify

(\frac{1}{2})^{2} : \frac{1}{4}

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= \frac{1}{4}

arccos (- 0.424)

\frac{3.2}{sin ( 24. 1 ^{\circ} )}

sin (2 0^{\circ}) + cos (4 0^{\circ}) - sin (16 0^{\circ}) + cos (14 0^{\circ})

cos^{2} (5 0^{\circ}) - sin^{2} (5 0^{\circ})

sin (30 0^{\circ} + 4 5^{\circ})

What is the value of cos^2(1/2*(2pi)/3) ?
The value of cos^2(1/2*(2pi)/3) is 1/4