What is the value of cot((25pi)/2) ?

The value of cot((25pi)/2) is 0

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cot((25pi)/2)

cot (\frac{25 π}{2})

0

Solution steps

cot (\frac{25 π}{2})

cot (\frac{25 π}{2}) = cot (\frac{π}{2})

cot (\frac{25 π}{2})

Rewrite

\frac{25 π}{2}

π \cdot 12 + \frac{π}{2}

= cot (π 12 + \frac{π}{2})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 12 + \frac{π}{2}) = cot (\frac{π}{2})

= cot (\frac{π}{2})

= cot (\frac{π}{2})

Use the following trivial identity:

cot (\frac{π}{2}) = 0

cot (\frac{π}{2})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 0

= 0

\frac{sin ( 0 )}{2}

arcsin (sin (- \frac{2 π}{3}))

tan (\frac{π}{6} - \frac{π}{4})

sin (arccos (1))

sin (26 0^{\circ})