Given $cottheta=-12/5$ and $270<theta<360$ , how do you find $csc (theta/2)$ ?

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Answer 1 · 2018-04-30T15:32:30

$rarrcsc(theta/2)=sqrt26$

Here, $270^(@)$ $<$ $theta$ $<$ $360^@$

$rarr135^(@)$ $<$ $theta/2$ $<$ $180^@$ It means $theta/2$ is in second quadrant where $sin and csc$ are positive.

$rarrcottheta=-12/5$

$rarrtantheta=-5/12$

$rarrcostheta=1/sectheta=1/sqrt(1+tan^2theta)=1/sqrt(1+(-5/12)^2)=12/13$

$rarrcsc(theta/2)=1/sin(theta/2)=1/sqrt((1-costheta)/2)=1/sqrt((1-12/13)/2)=1/sqrt(1/(26))=sqrt26$

Given cottheta=-12/5cottheta=-12/5 and 270<theta<360270<theta<360, how do you find csc (theta/2)csc (theta/2)?