What is the value of cos((3pi)/(12)) ?

The value of cos((3pi)/(12)) is (sqrt(2))/2

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cos((3pi)/(12))

cos (\frac{3 π}{12})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (\frac{3 π}{12})

Simplify:

\frac{3 π}{12} = \frac{π}{4}

\frac{3 π}{12}

Cancel the common factor:

3

= \frac{π}{4}

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

= \frac{2}{2}

20 cos (0)

cos (200 π)

arcsin (sin (\frac{17 π}{6}))

cos^{2} (\frac{5 π}{4})

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

What is the value of cos((3pi)/(12)) ?
The value of cos((3pi)/(12)) is (sqrt(2))/2