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Find an interval of values on the domain \([0,2\pi]\) for \(\theta \) that makes the follow ing set of statements true.

     a) \(csc\theta>0\) and \(cos{\theta}<0\)

 

     b) \(tan\theta<0\) and \(sec\theta>0\)

AdamTaurus  Jan 24, 2018
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 #1
avatar+85596 
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a)  csc θ > 0   and  cos θ < 0

 

csc is related to the sine.....so  the sine θ > 0   in Q1, Q2

And the cos θ < 0   in  Q2  and Q3

So.....the intersection of these is   Q2  ⇒  ( pi/2, pi)

 

b )   tan θ < 0   and  secθ > 0

 

tan θ < 0   in Q2 , Q4

An sec is related  to the cos.....so  cos θ > 0  in Q1 , Q4

So.....the intersection of these is  Q4 ⇒  (3pi/2, 2pi )

 

 

cool cool cool

CPhill  Jan 24, 2018
 #2
avatar+765 
+2

Thanks CPhill! Another good answer!

AdamTaurus  Jan 24, 2018

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