If sin theta = 3/5 and theta is acute how do you calculate cos theta and tan theta?

##costheta=4/5 and tantheta=3/4##.
We will use the Identity ## : sin^2theta+cos^2theta=1##.
##:. cos^2theta=1-sin^2theta=1-(3/5)^2=1-9/25=16/25##
##:. costheta=sqrt(16/25)=+-4/5##
But we know that theta is acute so it is in the first quadrant in which all the Trgo. ratios are ##+ve##
Hence ##costheta=+4/5##.
Finally ##tantheta=sintheta/costheta##…………..[Defn.]
##=(3/5)/(4/5)=3/4##