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If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
near zero
Yes. (Theta in radians, and then approximately, not exactly.)