Given sin(Θ) > 0 and tan(Θ) < 0 → in which quadrant/s Θ must reside?I’ve been having trouble with this question and have no idea where to start.
View attachment 34010
I know about exact ratio triangles and I assume that has something to do with it, but I’m not sure how it connects.
Thanks
Yes. Another way:(given by tan being negative and sin being positive)
Your diagram is not correct. You need to put the triangle on the x-y plane. That is draw the x and y axes and then put your triangle in the correct quadrant. If you do that and do the same work you did above you'll get the correct answer.View attachment 34012
Thats my working out so far. I've checked with the answers and it should be -5/root34, not positive. Is cos(Θ)=5/root34 negative because the angle is apparently in the second quadrant? (given by tan being negative and sin being positive)
Yes that's correct. I always ignore the signs at first when I draw the triangle. Then adjust the sign according to the quadrant.View attachment 34012
Thats my working out so far. I've checked with the answers and it should be -5/root34, not positive. Is cos(Θ)=5/root34 negative because the angle is apparently in the second quadrant? (given by tan being negative and sin being positive)
I see what you are saying, but as I replied to oliviak in previous post, I think it is ok to draw the triangle like she/he has, as long as you account for the sign later.Your diagram is not correct. You need to put the triangle on the x-y plane. That is draw the x and y axes and then put your triangle in the correct quadrant. If you do that and do the same work you did above you'll get the correct answer.