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

The value of cos((4pi)/6) is -1/2

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cos((4pi)/6)

cos (\frac{4 π}{6})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (\frac{4 π}{6})

Simplify:

\frac{4 π}{6} = \frac{2 π}{3}

\frac{4 π}{6}

Cancel the common factor:

2

= \frac{2 π}{3}

= cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 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}

arctan (tan (\frac{3 π}{4}))

- 3 sin (2 5^{\circ})

arccos (sin (\frac{5 π}{4}))

\frac{sin ( 1 0 ^{\circ} )}{cos ( 8 0 ^{\circ} )} + \frac{tan ( 2 0 ^{\circ} )}{cot ( 7 0 ^{\circ} )}

cos (\frac{20 π}{3})