What is the value of cos((25pi)/3) ?

The value of cos((25pi)/3) is 1/2

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cos((25pi)/3)

cos (\frac{25 π}{3})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

cos (\frac{25 π}{3})

cos (\frac{25 π}{3}) = cos (\frac{π}{3})

cos (\frac{25 π}{3})

Rewrite

\frac{25 π}{3}

2 π \cdot 4 + \frac{π}{3}

= cos (2 π 4 + \frac{π}{3})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 4 + \frac{π}{3}) = cos (\frac{π}{3})

= cos (\frac{π}{3})

= cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= \frac{1}{2}

tan (arctan (0.2))

4 \cdot cos (\frac{π}{4})

sin (2 \frac{3 π}{2})

4 (cos (\frac{2 π}{3}) + i sin (\frac{2 π}{3}))

3 arctan (1)