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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(2α)= cos2α – sin2α or 2cos2α - 1 or 1 – 2 sin2α 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 π/2 cos(π/2 – x)= sinx Cos(+)= -sinx Sin(–)= cosx Sin(+)= cosx Tan(-)= cotx Tan(+)= -cotx π Sin(π – x)= sinx Sin(π + x)= -sinx Cos(π – x)= -cosx Cos(π + x)= -cosx Tan(π – x)= -tanx Tan(π + x)= tanx Inverse Trig y=Sin-1: 1,4 -π/2 ≤ y ≤ π/2 & -1 ≤ x ≤ 1 (-90,90) y=Cos-1: 1,2 0 ≤ y ≤ π & -1 ≤ x ≤ 1 (0 ≤ Ѳ ≤ 180) y=Cot-1: 1,2 0 < y < π & x any real y=Tan-1: 1,4 -π/2 < y < π/2 & x any real (-90,+90) y=Sec-1: 1,2 0 ≤ y ≤ π, y≠π/2 & x≤-1 or x≥1 y=Csc-1: 1,2 -π/2 ≤ y ≤ π/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 π/2,0 π,-1 Sin graph: 0,0 π/2,1 π,0 3π/2,-1 2π,0

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