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

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Answer 1 · 2015-07-19T21:11:10

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

$sin (- x) = - sin (x)$ $sin(-x) = -sin(x)$ 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]}