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

1 Answer
Abhishek K.
Apr 30, 2018

#rarrcsc(theta/2)=sqrt26#

Explanation:

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#

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