How do you determine #sintheta# given #costheta=-2/3,90^circ<theta<180^circ#?

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Answer 1 · 2018-08-04T10:03:23

#sintheta=sqrt5/3#

Here ,

#90^circ < theta < 180^circ=>2^(nd)Quadrant=>sintheta > 0#

We know that,

#sin^2theta +cos^2theta=1#

#=>sin^2theta =1-cos^2theta ,where, costheta=-2/3#

#:.sin^2theta=1-(-2/3)^2=1-4/9=5/9#

#=>sintheta=sqrt(5/9)...to[because sintheta > 0]#

#:.sintheta=sqrt5/3#