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##