Evaluate in exact values: Sin(π/6 + π/2) can you please evaluate a different way than the book, without involving cosine?  I've attached 2 images of how I tried to solve.  Is this illigitimate?

Is there any serious difference between 5pi/3 and -pi/3? I had an online homework question that rejected 5pi/3 but would accept -pi/3. The question was to find angle y whose sine is -(sqrt(3)/2) and in the interval [-pi/2,pi/2]. Is the answer -pi/3 because of some negative value clockwise rotation about the unit circle, or is this just some program error?

Solve 2 sin? 0 – 9 sin 0 = 5 for 0 if 0° < 0 < 360°.

please i dont understand that you did after step 3 from 0=sin(2pi c)