How do you find the coterminal angle for $(11pi) / 4$ ?

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Answer 1 · 2015-07-15T23:49:42

Any angle of the form $(11pi)/4 + 2n pi$ with $n in ZZ$ is coterminal with $(11pi)/4$

The coterminal angle of $(11pi)/4$ in $[0, 2pi)$ is $(3pi)/4$

Coterminal angles are angles which are equal modulo $2 pi$

That is: $alpha$ and $beta$ are coterminal angles if $alpha - beta = 2n pi$ for some integer $n$ .

For example, $(11pi)/4$ and $(3pi)/4$ are coterminal, since:

$(11pi)/4 - (3pi)/4 = (8pi)/4 = 2pi = 2n pi$ with $n = 1$

Every angle has a unique coterminal angle in the range $[0, 2 pi)$

If $theta >= 0$ then $theta - 2 floor(theta/(2pi)) pi in [0, 2 pi)$

If $theta < 0$ then $theta + 2 ceil((-theta)/(2pi)) pi in [0, 2 pi)$

Coterminality is an example of an equivalence relation

If we use the symbol $~$ to mean "is coterminal with" then we find:

Reflexive: For all $alpha$ : $alpha ~ alpha$

Commutative: For all $alpha, beta$ : $alpha ~ beta <=> beta ~ alpha$

Transitive: For all $alpha$ , $beta$ , $gamma$ : if $alpha ~ beta$ and $beta ~ gamma$ then $alpha ~ gamma$

How do you find the coterminal angle for (11pi) / 4(11pi) / 4?