Fundamental Identities
Ifanequationcontainsoneormorevariablesandisvalidforallreplacementvaluesofthe
variablesforwhichbothsidesoftheequationaredefined,thentheequationisknownas
anidentity.Theequationx2+
Functions of General Angles
Acuteanglesinstandardpositionareallinthefirstquadrant,andalloftheirtrigonometric
functionsexistandarepositiveinvalue.Thisisnotnecessarilytrueofanglesingeneral.
Someofthesix
Graphs: Sine and Cosine
To see how the sine and cosine functions are graphed, use a calculator, a computer, or a set of trigonometry
tables to determine the values of the sine and cosine functions for
Law of Cosines
Theprevioussectioncoveredthesolvingofrighttriangles.Inthissection,andthenext,you
seeformulasthatcanbesolveanytriangle.If,andaretheanglesofany(right,acute,
orobtuse)triangle,anda,b,andca
Law of Sines
ThefollowingdiscussioncentersaroundFigure1.
Figure1
ReferencetrianglesforLawofSines.
LinesegmentCDisthealtitudeineachfigure.ThereforeACDandBCDareright
triangles.Thus,
InFigure(b),CBDhasth