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Mathematics LibreTexts

14: Appendix

  • Page ID
    126245
  • ( \newcommand{\kernel}{\mathrm{null}\,}\)

    Graphs of the Parent Functions

    CNX_Precalc_Figure_APP_001.jpg
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    Graphs of the Trigonometric Functions

    CNX_Precalc_Figure_APP_004n.jpg
    Figure_APP_005.jpg" style="width: 975px; height: 513px;" width="975px" height="513px" src="https://math.libretexts.org/@api/dek...re_APP_005.jpg" />
    CNX_Precalc_Figure_APP_006n.jpg
    Figure_APP_007n.jpg" style="width: 975px; height: 444px;" width="975px" height="444px" src="https://math.libretexts.org/@api/dek...e_APP_007n.jpg" />

    Trigonometric Identities

    Pythagorean Identities cos2t+sin2t=11+tan2t=sec2t1+cot2t=csc2t
    Even-Odd Identities cos(t)=costsec(t)=sectsin(t)=sinttan(t)=tantcsc(t)=csctcot(t)=cott
    Cofunction Identities cost=sin(π2t)sint=cos(π2t)tant=cot(π2t)cott=tan(π2t)sect=csc(π2t)csct=sec(π2t)
    Fundamental Identities tant=sintcostsect=1costcsct=1sintcott=1tant=costsint
    Sum and Difference Identities cos(α+β)=cosαcosβsinαsinβcos(αβ)=cosαcosβ+sinαsinβsin(α+β)=sinαcosβ+cosαsinβsin(αβ)=sinαcosβcosαsinβtan(α+β)=tanα+tanβ1tanαtanβtan(αβ)=tanαtanβ1+tanαtanβ
    Double-Angle Formulas sin(2θ)=2sinθcosθcos(2θ)=cos2θsin2θcos(2θ)=12sin2θcos(2θ)=2cos2θ1tan(2θ)=2tanθ1tan2θ
    Half-Angle Formulas sinα2=±1cosα2cosα2=±1+cosα2tanα2=±1cosα1+cosαtanα2=sinα1+cosαtanα2=1cosαsinα
    Reduction Formulas sin2θ=1cos(2θ)2cos2θ=1+cos(2θ)2tan2θ=1cos(2θ)1+cos(2θ)
    Product-to-Sum Formulas cosαcosβ=12[cos(αβ)+cos(α+β)]sinαcosβ=12[sin(α+β)+sin(αβ)]sinαsinβ=12[cos(αβ)cos(α+β)]cosαsinβ=12[sin(α+β)sin(αβ)]
    Sum-to-Product Formulas sinα+sinβ=2sin(α+β2)cos(αβ2)sinαsinβ=2sin(αβ2)cos(α+β2)cosαcosβ=2sin(α+β2)sin(αβ2)cosα+cosβ=2cos(α+β2)cos(αβ2)
    Law of Sines sinαa=sinβb=sinγcasinα=bsinβ=csinγ
    Law of Cosines a2=b2+c22bccosαb2=a2+c22accosβc2=a2+b22abcosγ

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