Question

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

Answer 1

We will use the Identity :sin2θ+cos2θ=1.

∴cos2θ=1−sin2θ=1−(35)2=1−925=1625

∴cosθ=√1625=±45

But we know that theta is acute , so, it is in the first quadrant, in which, all the Trgo. ratios are +ve

Hence, cosθ=+45.

Finally, tanθ=sinθcosθ..............[Defn.]

=3545=34