What is the value of cos((21pi)/2) ?

The value of cos((21pi)/2) is 0

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cos((21pi)/2)

cos (\frac{21 π}{2})

0

Solution steps

cos (\frac{21 π}{2})

cos (\frac{21 π}{2}) = cos (\frac{π}{2})

cos (\frac{21 π}{2})

Rewrite

\frac{21 π}{2}

2 π \cdot 5 + \frac{π}{2}

= cos (2 π 5 + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 5 + \frac{π}{2}) = cos (\frac{π}{2})

= cos (\frac{π}{2})

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

= 0

arccos (\frac{3}{12})

8 + 4 cos (\frac{π}{2})

arcsin (\frac{1.33}{2.1})

2 sin (\frac{π}{2}) cos (\frac{π}{2})

0.23 \cdot 0.0133 \cdot cos (53. 1^{\circ})