`g(x) = cot(x)` Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The graph of g(x)=cot(x) is shown below.

We know that sin(-x)=-sin(x) and cos(-x)=cos(x).

So, `cot(-x)=\frac{cos(-x)}{sin(-x)}=\frac{cos(x)}{-sin(x)}=-cot(x)`

Hence, cot (x) is an odd function, and its graph is symmetric with respect to the origin.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Image (1 of 1)
Approved by eNotes Editorial