Question #306567

Find the quadrant in which 𝑃(𝑡) lies if 𝑠𝑒𝑐 𝑡 > 0 and 𝑐𝑠𝑐 𝑡 < 0.


1
Expert's answer
2022-03-07T17:08:03-0500



csc t = 1/sin t

 

sec t = 1/ cos t


From the above illustration;

sin t < 0 in the 3rd and 4th Quadrant

and cos t >0 in the 1st and 4th Quadrant.


Therefore,

When sec t > 0  cos t > 0

and when csc t <0  sin t < 0


 𝑃(𝑡) lies in the quadrant on which the two relations overlap each other

hence,

 𝑃(𝑡) is in the 4th Quadrant [Answer]


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