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sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o
sin theta = opp/hyp sin 45 = opp/1 opp = sin 45 = sqrt(2)/2 ~= 0.7071
The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
One relationship is: cos(x) = sin(90° - x) if you use degrees. Or in radians: cos(x) = sin(pi/2 - x) Another relationship is the pythagorean identity.
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.