APL(NARS), 116 chars

r←a C w;d;v;m;p
r←d←1+(2≠↑a)×w-1⋄m←w×wׯ1⋄p←2⊃a⋄v←0 1-(2=↑a)
→0×⍳0≥p-←1⋄r+←d×←m÷×/v+←2⋄→2

z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z

15+44+28+2+27=116

the last line call the function C that is a sin and cos function depend of input (input ≠2 is sin input =2 is cos)

      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      5 3
 10.208333
 14.541667
      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      8.555 13
 0.765431
 ¯0.641092
      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      9.26 10
 ¯3.154677
 ¯8.404354
      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      6.54 12
 0.253986
 0.967147
      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      5 1
 5.000000
 1.000000
      z←⎕⋄6⍕1 z[2]C↑z⋄6⍕2 z[2]C↑z 
⎕:
      20 20
 ¯5364.411846
 ¯10898.499385

OT it would be possible to calculate the exact answer using rationals and input rational

      z←⎕⋄1 z[2]C↑z⋄2 z[2]C↑z 
⎕:
      1r4  10
8264318085745811128158727r33404146443928530321408000 
17051609536099989115458551r17598710837038136237752320