What is the value of cos((39pi)/6) ?

The value of cos((39pi)/6) is 0

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cos((39pi)/6)

cos (\frac{39 π}{6})

0

Solution steps

cos (\frac{39 π}{6})

Simplify:

\frac{39 π}{6} = \frac{13 π}{2}

\frac{39 π}{6}

Cancel the common factor:

3

= \frac{13 π}{2}

= cos (\frac{13 π}{2})

cos (\frac{13 π}{2}) = cos (\frac{π}{2})

cos (\frac{13 π}{2})

Rewrite

\frac{13 π}{2}

2 π \cdot 3 + \frac{π}{2}

= cos (2 π 3 + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + \frac{π}{2}) = cos (\frac{π}{2})

= cos (\frac{π}{2})

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

= 0

cos (0.32)

arctan (\frac{3 3}{6})

arctan (\frac{375}{500})

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

sin (\frac{π}{3}) + cos (\frac{π}{6})