Use the rated acute angle to state an equivalent expression

Tan110

The answer is tan290. Why isn't it 70? Please explain

tan 110 is negative (-2.75)

tan 70 is positive ( +2.75)
to have negatve tangent the angle must be in quadrants 2 or 4
tan 290 = -2.75 same as tan 110

How would you figure it out using a Cartesian plane?

And assuming you didn't know the answer was tan290, how would you get tan290 (because I'm supposed to arrive at the answer without knowing the answer..)?? Because the question is just asking for the equivalent expression of tan110, I just got tan70, which is why I wanted to know why that didn't work.

Okay, that seems really confusing. So in essence, I really just want to know how to find the equivalent expression using the related acute angle, tan110

Sorry, I still don't understand... I know I seem really dumb right now, but this unit just isn't working for me for some reason.. I'm usually pretty decent at math. We just started grade 11 trig and I'm totally lost after the first lesson.

I understand that it's in quadrant four, but how did you know that tan110 was equal to tan290? I mean, if I never told you the answer was tan290, how would you have arrived at the answer? I'm sure you wouldn't just do it by trial and error. I feel like I'm just missing a really simple concept here...

90 + 20 = 110

90 - 20 = 70
270 - 20 = 250
270 + 20 = 290

Preferably in terms of a Cartesian plane.

I gave you the plane

110 is in quadrant 2
x - negative, y is positive

you need the other quadrant where x and y have opposite signs

that is quadrant 4 where x is positve and y is negative

sketch it on your x y plane !

I did 20 degrees off the y axis in all four quadrants. The tan is negative in quadrants 2 and four

I could have done 70 degrees off the x axis in all four quadrants just as well.

Ohhh. Wow, I finally get it, haha. Thank you!! I honestly just have one more question... 5 minutes;