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Popular >

cos(2pi2)

Solution

cos (2 \cdot π \cdot 2)

Solution

1

Solution steps

cos (2 π 2)

Simplify

= cos (4 π)

cos (4 π) = cos (0)

cos (4 π)

Rewrite

4 π

as

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

Popular Examples

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arccos(7/(sqrt(83)))

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arctan((2200+1650)/(15000))

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\frac{90}{cos ( 3 0 ^{\circ} )}

cos (2 π)

Frequently Asked Questions (FAQ)

What is the value of cos(2*pi*2) ?
The value of cos(2*pi*2) is 1