How do you determine #cottheta# given #csctheta=sqrt11/3,pi/2<theta<pi#?

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Answer 1 · 2018-07-12T09:27:30

#cot theta=-sqrt2/3#

Here,

#csctheta=sqrt11/3#

Where, #pi/2 < theta < pi=>II^(nd)Quadrant=>color(red)(cot theta <0#

We know that ,

#csc^2theta-cot^2theta=1#

#=>cot^2theta=csc^2theta-1=11/9-1=2/9#

#=>cot^2theta=(sqrt2/3)^2 #

#=>cot theta=-sqrt2/3to[because color(red)(cottheta < 0)]#