Are sine, cosecant, tangent, and cotangent odd function?

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Answer 1 · 2015-07-19T21:11:10

Yes, they all satisfy #f(-x) = -f(x)# for all #x# in their respective domains.

#sin(-x) = -sin(x)# for all #x in RR#

graph{sin x [-10, 10, -5, 5]}

#csc(-x) = -csc(x)# for all #x in RR "\" { n pi : n in ZZ }#

graph{csc x [-10, 10, -5, 5]}

#tan(-x) = -tan(x)# for all #x in RR "\" { pi/2+n pi : n in ZZ }#

graph{tan x [-10, 10, -5, 5]}

#cot(-x) = -cot(x)# for all #x in RR "\" { n pi : n in ZZ }#

graph{cot x [-10, 10, -5, 5]}