If cos 0=0.3090 which of the following represents approximate values of sin 0 and tan 0, for 0 degrees< 0< 90 degrees?

Step-by-step explanation:

Please use the word "theta" or an actual Greek letter to denote angle.  Even tho' I catch your drift, your "cos 0 = 0.3090" was at first confusing.

Keep in mind the following facts:  

(sin theta)^2 + (cos theta)^2 = 1

tan theta = sin theta  /  cos theta

Thus, if we start with cos theta = 0.3090, and want sin theta, we use the Pythagorean Theorem:  (sin theta)^2 = 1 - (cos theta)^2.

Here, (sin theta)^2 = 1 - (0.3090)^2

                               = 1 - 0.0955, or 0.9045.  

                                   Thus, sin theta +√0.9045 = +0.9511.

We now know both sin theta and cos theta, and can easily find tan theta from the formula above:

                    sin theta        0.9511

tan theta = = = 3/-880

                    cos theta        0.3090

The second answer is the correct one.