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

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

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cos(pi 1/6)

cos (π \frac{1}{6})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

cos (π \frac{1}{6})

Simplify:

π \frac{1}{6} = \frac{π}{6}

π \frac{1}{6}

Multiply fractions:

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

= \frac{1 π}{6}

Multiply:

1 π = π

= \frac{π}{6}

= 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}

= \frac{3}{2}

sec (arcsin (\frac{2}{5}))

4 cos^{2} (16 5^{\circ}) - 2

sin (3 0^{\circ}) + sin (12 0^{\circ}) + cos (24 0^{\circ}) - cos (33 0^{\circ})

arctan (sin (\frac{11 π}{4}))

cos (54. 7^{\circ})