A function is defined to be even if it meets the following condition;
[tex]f(x)=f(-x)[/tex]
Meaning it is symmetrical about the y-axis.
A functiion is defined to be odd if it meets the condition;
[tex]f(-x)=-f(x)[/tex]
And neither even or odd if it doesnt meet any of the above criteria.
Let us look at sinx.
A well known theorem from sin trigonometry is;
[tex]\sin (-x)=-\sin x[/tex]
Therefore, sinx is an odd function.
Let us look at cotx.
cot x is defined as;
[tex]\cot x=\frac{\cos x}{\sin x}[/tex]
cosx is an even function, sinx however is odd, so cotx is odd.
Therefore, cotx is an odd function.
