Question

theta, given cos 2 theta =3/5 and theta terminates in quadrant I

Answer 1

Half angle identities is all it takes ...
\[\Large \cos\left(\frac \alpha 2\right)= \pm\sqrt{\frac{1+\cos(\alpha)}{2}}\]

Answer 2

use identities ti find the exact values of sine and cosine

Answer 3

Yes, well, here's a little something to get you started :
\[\Large \cos(\theta) = \cos\left(\frac{2\theta}2\right)= \pm\sqrt{\frac{1+\color{red}{\cos(2\theta)}}2}\]

Answer 4

And... you are, in fact, GIVEN the value of \(\large \color{red}{\cos(2\theta)}\)