What is the value of 2sqrt(3)cos(pi/6) ?

The value of 2sqrt(3)cos(pi/6) is 3

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2sqrt(3)cos(pi/6)

23 cos (\frac{π}{6})

3

Solution steps

23 cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= 23 \frac{3}{2}

Simplify

23 \frac{3}{2} : 3

23 \frac{3}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 33

Apply radical rule:

a a = a

33 = 3

= 3

= 3

- i \cdot ln (sin (e^{i \cdot 2 \cdot π}))

arctan (\frac{- 5 3}{5})

\frac{12 \cdot sin ( 6 3 ^{\circ} )}{sin ( 8 0 ^{\circ} )}

sec (\frac{3}{2} π)

sinh (\frac{π}{4})