Sin(10)*12 = 12*sin(10) = 12*0.1736 = 2.0838, approx.
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A 12/12 is 45 degrees. If you set a 45 degree piece of wood on the roof it should be level.
In angle measurement, 60 minutes = 1° 57° 12' = 57.2 ° Sin 57.2 = 0.84057 (5dp)
A roof angle of 6 degrees = 1.26 / 12 rise or pitch.
A 10/12 means for every foot of run your rise is 10". so, 10' x 10" = 100" rise in 10 feet.
Trigonometry includes 12 baisic functions. Sine, Cosine, and Tangent are the three most baisic. Each of those functions has a reciprocal. Cosine's reciprocal is Secant, Sine reciprocal is Cosecant, and Tangent's reciprocal is Cotangent. Each of those six functions has an inverse funcion called Inverse Sine, Cos etc... or Arcsine, Arcosine, Arcsecant, etc.... The shorthand for each function is sin, caos, tan, sec, csc, cot. The inverses have a -1 notation like sin-1.