# Quick trig question

Hi, can someone help me with this please?

“Given that theta is acute, express in terms of tan theta:

tan (- theta)”

I used the graph to get -tan(theta) which is correct but can someone tell me/direct me to the rules that can help me do these without the graph?

Is it just that the - from the angle is put before the function? Are there any limitations of this rule etc?
tan is an ODD function
Original post by the bear
tan is an ODD function

What does that mean? Odd?
Original post by subbhy
What does that mean? Odd?

[Definition] A function is odd if f(-x) = -f(x), and it's even if f(-x) = f(x).

Now back to your question. For the most part it is useful to remember by heart. But if you can't, hopefully you remember
sin(-x) = -sin(x) [i.e. odd] and cos(-x) = cos(x) [i.e. even].
Then use tan(x) = sin(x) / cos(x).

In fact, these holds for all real values of x. We don't need the angle to be acute.
Original post by tonyiptony

[Definition] A function is odd if f(-x) = -f(x), and it's even if f(-x) = f(x).

Now back to your question. For the most part it is useful to remember by heart. But if you can't, hopefully you remember
sin(-x) = -sin(x) [i.e. odd] and cos(-x) = cos(x) [i.e. even].
Then use tan(x) = sin(x) / cos(x).

In fact, these holds for all real values of x. We don't need the angle to be acute.

Thanks, so these rules work for every angle including negatives?
Original post by subbhy
Thanks, so these rules work for every angle including negatives?

yes, as long as the angle is in the domain of the function