By itself, sin theta has no use at all. Similarly, there is no use for the number 14. It is only in the context of something, or things, that measure that value is there any sue for it.
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The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
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.
sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o
The identity for tan(theta) is sin(theta)/cos(theta).
It is not! So the question is irrelevant.