Question

I really need help solving this having trouble getting an answerThis is from my ACT prep guide onlineI will attach another image

Answer 1

A function is defined to be even if it meets the following condition;

`f(x)=f(-x)`

Meaning it is symmetrical about the y-axis.

A functiion is defined to be odd if it meets the condition;

`f(-x)=-f(x)`

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;

`\sin (-x)=-\sin x`

Therefore, sinx is an odd function.

Let us look at cotx.

cot x is defined as;

`\cot x=(\cos x)/(\sin x)`

cosx is an even function, sinx however is odd, so cotx is odd.

Therefore, cotx is an odd function.