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?

Reply 1

the bear

20

tan is an ODD function

Reply 2

subbhy

OP

18

Original post by the bear

tan is an ODD function

What does that mean? Odd?

Reply 3

tonyiptony

11

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.

Reply 4

subbhy

OP

18

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.