Finding the two possible values of an angle

Sep 2016
19
0
ottawa
Hi,

I was asked to find the two possible values of (TanA = -2/6), but I'm having some trouble here. In my text, it says the related acute angle is the angle between the terminal arm and the closest part of the x-axis. That would lead me to believe that if the acute angle is 18.43 degrees, then the angle in quadrant II would be 180 - 18.43 = 161.57. And in quadrant IV, 360 - 18.43 = 341.57.

This doesn't seem right to me. When I plot it on a grid, the acute angle in quadrant II is 18.43 degrees from the y-axis. In this case the angle would be 108.43 degrees. My lesson text wasn't very clear on this and I don't have any way of communicating with a teacher. I would greatly appreciate any help and clarification.

math work.jpg

Here's my written work, I apologize for the sloppiness.

Thanks again.
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey jpompey.

I'd suggest you trying to check your answer independently with a calculator or computer program so that you can independently verify it yourself.
 

romsek

MHF Helper
Nov 2013
6,666
3,005
California
Clipboard01.jpg

$\theta$ are the two angles $-\pi < \theta \leq \pi$ that will have $\tan(\theta) = \dfrac{-2}{6}$

remember that $\dfrac{-2}{6} = \dfrac{2}{-6}$

They happen to be $\theta = -18.435^\circ,~~\theta = -18.435^\circ + 180^\circ = 161.565^\circ$
 
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Sep 2016
19
0
ottawa
Thank you very much, that completely escaped my mind. I appreciate your help.
 
Sep 2017
1
0
USA
What a proper solution of the question! Thanks for being so sincere with us!