What is the value of cos((25pi)/4) ?

The value of cos((25pi)/4) is (sqrt(2))/2

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cos((25pi)/4)

cos (\frac{25 π}{4})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (\frac{25 π}{4})

cos (\frac{25 π}{4}) = cos (\frac{π}{4})

cos (\frac{25 π}{4})

Rewrite

\frac{25 π}{4}

2 π \cdot 3 + \frac{π}{4}

= cos (2 π 3 + \frac{π}{4})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

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

= cos (\frac{π}{4})

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

= \frac{2}{2}

2 (sin (4) + cos (4) + 4 (cos (4) - sin (4)))

1 - \frac{sin ( 4 5 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

tan^{2} (6 0^{\circ}) - sec^{2} (6 0^{\circ}) + cot (4 5^{\circ})

cos (arctan (2))

sin (\frac{2 π}{3}) - cos (\frac{π}{12}) + tan (\frac{5 π}{4})