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- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 113
- Dewitt
- math 113 notes.docx

James P.

Identity Sum & Diff Tan (x ?? y)= ( tanx ?? tany ) / ( 1 ?? tanx tany) Cos (x?? y) = cosx cosy ?? sinx siny Sin (x ?? y) = sinx cosy ?? cosx siny Double < tan (2x) = 2tanx / 1-tan2x or 2cotx / cot2x-1 or 2 / cotx-tanx Sin(2x)=2sinx cosx Cos(2?)= cos2? ? sin2? or 2cos2? - 1 or 1 ? 2 sin2? Half < Sin (x/2 ) = ± sqrt ( 1-cosx / 2) cos (x/2) = ± sqrt (1+cosx / 2) Tan (x/2) = 1 - cosx / sinx or sinx / 1+cosx or ± sqrt 1-cosx / 1+cosx Ratio Tan= sin / cos Cot= cos / sin Pythag Sin2 + Cos2= 1 1 + tan2= sec2 1 + cot2= csc2 Reduction Cos(-x)=cosx Sin*= -sinx Csc*= -cscx Tan*= -tanx Sec*=secx Cot*= -cotx ?/2 cos(?/2 ? x)= sinx Cos(+)= -sinx Sin(?)= cosx Sin(+)= cosx Tan(-)= cotx Tan(+)= -cotx ? Sin(? ? x)= sinx Sin(? + x)= -sinx Cos(? ? x)= -cosx Cos(? + x)= -cosx Tan(? ? x)= -tanx Tan(? + x)= tanx Inverse Trig y=Sin-1: 1,4 -?/2 ? y ? ?/2 & -1 ? x ? 1 (-90,90) y=Cos-1: 1,2 0 ? y ? ? & -1 ? x ? 1 (0 ? ? ? 180) y=Cot-1: 1,2 0 < y < ? & x any real y=Tan-1: 1,4 -?/2 < y < ?/2 & x any real (-90,+90) y=Sec-1: 1,2 0 ? y ? ?, y??/2 & x?-1 or x?1 y=Csc-1: 1,2 -?/2 ? y ? ?/2, y?0 & x?-1 or x?1 * sin=y/r cos=x/r tan=y/x csc=r/y sec=r/x cot=x/y a2?b2=(a+b)(a-b) (1?b2)=(1?b)(1+b) (a+b)2=a2+b2+2ab (a?b)2=a2+b2?2ab *cos graph: 0,1 ?/2,0 ?,-1 Sin graph: 0,0 ?/2,1 ?,0 3?/2,-1 2?,0

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