Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

14: Appendix

( \newcommand{\kernel}{\mathrm{null}\,}\)

Graphs of the Parent Functions

CNX_Precalc_Figure_APP_001.jpg
Figure_APP_002.jpg" style="width: 975px; height: 430px;" width="975px" height="430px" src="/@api/deki/files/7714/CNX_Precalc_Figure_APP_002.jpg" />

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="/@api/deki/files/7717/CNX_Precalc_Figure_APP_005.jpg" />
CNX_Precalc_Figure_APP_006n.jpg
Figure_APP_007n.jpg" style="width: 975px; height: 444px;" width="975px" height="444px" src="/@api/deki/files/7719/CNX_Precalc_Figure_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

This page titled 14: Appendix is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

  • Was this article helpful?

Support Center

How can we help?