What is the value of cot(-(11pi)/4) ?

The value of cot(-(11pi)/4) is 1

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cot(-(11pi)/4)

cot (- \frac{11 π}{4})

1

Solution steps

cot (- \frac{11 π}{4})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{11 π}{4}) = - cot (\frac{11 π}{4})

= - cot (\frac{11 π}{4})

cot (\frac{11 π}{4}) = cot (\frac{3 π}{4})

cot (\frac{11 π}{4})

Rewrite

\frac{11 π}{4}

π \cdot 2 + \frac{3 π}{4}

= cot (π 2 + \frac{3 π}{4})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

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

= cot (\frac{3 π}{4})

= - cot (\frac{3 π}{4})

Use the following trivial identity:

cot (\frac{3 π}{4}) = - 1

cot (\frac{3 π}{4})

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

= - 1

= - (- 1)

Simplify

= 1