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Popular >

cos((6pi)/3)

Solution

cos (\frac{6 π}{3})

Solution

1

Solution steps

cos (\frac{6 π}{3})

Simplify

= cos (2 π)

cos (2 π) = cos (0)

cos (2 π)

Rewrite

2 π

as

2 π + 0

= cos (2 π + 0)

Apply the periodicity of

cos

:

cos (x + 2 π) = cos (x)

cos (2 π + 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

Popular Examples

arcsin (- 0.7)

csc (- 15 0^{\circ})

arctan(tan((11pi)/6))

arctan (tan (\frac{11 π}{6}))

arcsin(1/(sqrt(5)))

arcsin (\frac{1}{5})

arctan((1.5)/2)

arctan (\frac{1.5}{2})

Frequently Asked Questions (FAQ)

What is the value of cos((6pi)/3) ?
The value of cos((6pi)/3) is 1