Question 650303: Hi,
I am just beginning Precalculus and am looking at two short statements of the same nature - the instructions ask me to tell whether the trigonometric function is positive, negative, 0, or undefined. I am confused about what qualifies a trigonometric function as any of these. I am looking at these two:
csc (2pi/3) and (sec450º)
I managed to get both undefined but I do not know how, and I doubt that is correct. If somebody could please explain to me how to tell what the nature of these problems are, I would really appreciate it!
-Alex
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! csc (2pi/3) and (sec450º)
Each circle contains 360º or 2π radians divided into 4 quadrants.
All you need to do is determine which quadrant the angle is in from which you can determine its sign as follows:
quadrant I:
all functions>0
..
quadrant II
sin and csc >0
cos and sec<0
tan and cot<0
..
quadrant III
sin and csc <0
cos and sec<0
tan and cot>0
..
quadrant IV
sin and csc <0
cos and sec>0
tan and cot<0
..
csc (2pi/3) is in quadrant II, therefore, its sign>0
sec450ºis going around the circle once and ending at 90º or π/2
sec 450º=1/cos450º=1/cos90º=1/0=undefined
hope this helps
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