Question 1029138: I am supposed to circle the location (s) for the terminal side of each angle given (in standard position). The choices are: quadrant I, II, III, IV, and quadrantal angle. I am having trouble with a) sec theta <0. I think it's in quadrants I and II, but I'm not certain if it's a quadrantal angle also??? And, b) tan theta 0. I am pretty sure they are both in quadrant IV, but not sure about the quadrantal angle on this one either. Any help would be appreciated! Thanks!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part (A)
secant = 1/cosine so this means that if sec(theta) < 0, then cos(theta) < 0
Cosine is negative in quadrants II and III where the x coordinate of an ordered pair point is negative (eg: (-2, 5))
So sec(theta) < 0 only happens in Q2 or Q3
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Part (B)
You wrote "tan(theta) 0" but you forgot to put a symbol between the "tan(theta)" and the "0". So I have no idea if it's < or >. There isn't enough info to answer this problem.
IF it's tan(theta) > 0 then the answer would be Q1 and Q3 (since sine&cosine are both either together positive or together negative)
IF it's tan(theta) < 0 then the answer would be Q2 and Q4 (sine&cosine have different signs. One is positive, the other is negative)
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