(3) If sin theta =3/4
then find cos theta and tan theta
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We know that,
sin^2 theta +cos^2 theta=1
(3/4)^2+cos^2 theta=1
(9/16)+cos^2 theta=1
cos^2 theta=1-9/16
cos^2 theta=(16-9)/16
cos^2 theta =7/16
cos theta= (root 7)/16
We also know that,
tan theta= sin theta/cos theta
tan theta=(3/4)/(root 7/16)
=(3/4)*(16/root7)
=12/root 7
sin^2 theta +cos^2 theta=1
(3/4)^2+cos^2 theta=1
(9/16)+cos^2 theta=1
cos^2 theta=1-9/16
cos^2 theta=(16-9)/16
cos^2 theta =7/16
cos theta= (root 7)/16
We also know that,
tan theta= sin theta/cos theta
tan theta=(3/4)/(root 7/16)
=(3/4)*(16/root7)
=12/root 7
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