What is the value of sqrt(4cos(2*pi/6)) ?

The value of sqrt(4cos(2*pi/6)) is square root of 2

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sqrt(4cos(2*pi/6))

4 cos (2 \cdot \frac{π}{6})

2

Decimal Notation

1.41421 \dots

Solution steps

4 cos (2 \cdot \frac{π}{6})

Rewrite using trig identities:

cos (2 \cdot \frac{π}{6}) = \frac{1}{2}

cos (2 \cdot \frac{π}{6})

Simplify:

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= cos (\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}

= 4 \cdot \frac{1}{2}

Simplify

4 \cdot \frac{1}{2} : 2

4 \cdot \frac{1}{2}

Multiply

4 \cdot \frac{1}{2} : 2

4 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= 2

= 2

tan^{2} (4 5^{\circ} - 1 6^{\circ})

sin (4 5^{\circ}) 12

- e^{c o s (0)} sin (0)

arctan (\frac{5.54}{9.8} + 0.2)

20 sin (7 5^{\circ})

What is the value of sqrt(4cos(2*pi/6)) ?
The value of sqrt(4cos(2*pi/6)) is square root of 2