What is the value of cos(5pi 1/6) ?

The value of cos(5pi 1/6) is -(sqrt(3))/2

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cos(5pi 1/6)

cos (5 π \frac{1}{6})

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

cos (5 π \frac{1}{6})

Simplify:

5 π \frac{1}{6} = \frac{5 π}{6}

5 π \frac{1}{6}

Multiply fractions:

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

= \frac{1 \cdot 5 π}{6}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5 π}{6}

= cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 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}

= - \frac{3}{2}

\frac{sin ( 4 5 ^{\circ} ) + csc ^{2} ( 6 0 ^{\circ} )}{cos ( 3 0 ^{\circ} ) - tan ^{2} ( 4 5 ^{\circ} )}

sin (16.2 6^{\circ})

0.2 cos (3 0^{\circ})

arctan (0.37)

arctan (- \frac{9}{8})