SOLUTION: State the quadrant of the terminal side of q if csc(q) < 0 and tan(q) > 0

Algebra ->  Trigonometry-basics -> SOLUTION: State the quadrant of the terminal side of q if csc(q) < 0 and tan(q) > 0      Log On


   

Question 1084359: State the quadrant of the terminal side of q if csc(q) < 0 and tan(q) > 0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
My answer is the 3rd quadrant
+csc%28q%29+%3C+0+
+csc%28q%29+=+1%2Fsin%28q%29+
Both sides are negative, so +sin%28q%29+ is negative.
The sine function is negative in the 3rd and 4th quadrants
--------------------------
+tan%28q%29+%3E+0+
+sin%28q%29+%2F+cos%28q%29+%3E0+
Since I am already limited to the 3rd and 4th quadrants,
The terminal end of +q+ must be in the 3rd quadrant
where both sine and cosine functions are negative
(-) / (-) = (+)