SOLUTION: I'm having trouble figuring this out and think it's a matter of what I'm inputting? Determine the quad in which the terminal side of "a" lies, subject to the conditions that tan

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Question 288206: I'm having trouble figuring this out and think it's a matter of what I'm inputting?
Determine the quad in which the terminal side of "a" lies, subject to the conditions that tan a <0
cos a>0 ?
How am I suppose to this, by graphing I assume as I have to figure which quadrant, but how do I graph a problem such as this?
Thanks,
Nathalie
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that tan%28x%29=sin%28x%29%2Fcos%28x%29. So if tan%28a%29%3E0, then sin%28a%29%2Fcos%28a%29%3E0. Now because we already know that cos%28a%29%3E0, we can multiply both sides of sin%28a%29%2Fcos%28a%29%3E0 by cos%28a%29 to get sin%28a%29%3E0 (and we don't have to worry about if the sign will flip or not).


So if tan%28a%29%3E0 and cos%28a%29%3E0, then sin%28a%29%3E0 as well. Recall that the cosine of a given angle will produce the 'x' value of the terminal side on the unit circle. So if cos%28a%29%3E0, then we can say that x%3E0 for the given point (x,y) which is the endpoint of the terminal side.


Similarly if sin%28a%29%3E0, then y%3E0 (since sine is associated with the 'y' value of the point on the unit circle). This means that both 'x' and 'y' are positive which places the terminal side in the first quadrant.