What is the value of cot((-3pi)/4) ?

The value of cot((-3pi)/4) is 1

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cot((-3pi)/4)

cot (\frac{- 3 π}{4})

1

Solution steps

cot (\frac{- 3 π}{4})

Simplify

= cot (- \frac{3 π}{4})

Use the following property:

cot (- x) = - cot (x)

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

cos (arccos (- \frac{3}{2}))

arccos (cos (\frac{7 π}{2}))

arccos (90)

cos (8 3^{\circ})

arcsin (- 6)