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

2 Answers
Deepak G.
Jul 26, 2016

#costheta=4/5#
#tantheta=3/4#

Explanation:

#sintheta=3/5#
#costheta=sqrt(1-sin^2theta#
or
#costheta=sqrt(1-(3/5)^2)#
or
#costheta=sqrt(1-9/25#
or
#costheta=sqrt((25-9)/25)#
or
#costheta=sqrt(16/25)#
or
#costheta=4/5#------------Ans #1#

#tantheta=sintheta/costheta#
or
#tantheta=(3/5)/(4/5)#
or
#tantheta=3/4#-------------Ans #2#

Ratnaker Mehta
Jul 26, 2016

#costheta=4/5, and, tantheta=3/4#.

Explanation:

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#

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