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

The value of cos((12pi)/3) is 1

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cos((12pi)/3)

cos (\frac{12 π}{3})

1

Solution steps

cos (\frac{12 π}{3})

Simplify

= cos (4 π)

cos (4 π) = cos (0)

cos (4 π)

Rewrite

4 π

2 π \cdot 2 + 0

= cos (2 π 2 + 0)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 2 + 0) = cos (0)

= cos (0)

= cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= 1

sec (- 2)

sin (2 \cdot 45)

- 4 cos (\frac{3 π}{4})

tan (\frac{π}{4}) - tan (0)

arcsin (7)