Trigonometria

Yt"¡u lrnvs probatrly seeü the ¡Jefinitions of thr trigon{iftetrii funetisns based 6n
right triangles Figure 1 sumnlarizes the definitions of the sine. cosine. and tange¡tfunctions. You should review Figure I carefull¡,. becau$c these concepts are neüed
far n'rany applicaticn-r later in this book.
More generalll'. we define thetrigonometric functirrns based on the unit circle.
Thc unit circle, which we denore h1, C.. is the circle u.ith radius I and center rt thc
origin:it has equation xl + .u3 - l. [.et ¡lhe the point (1,0) anil let rbe a p(]sitive
Erimtrrr, Therg is a ringle point P cn the circle C such lhsf the djstance. mrasured
in the cor¡¡¡J¿rrrloclei$¡'se directionaround the arc ép. is equal ta r. {see Figure ?.J
Recall ih¡t the circumference of a circle with radius r is 2¡¡¡. su the circumference
¡f c is 2¡r.Thus" if i : tr. then thepoint P is exucrly halfuay around the circle frr¡nl
the grgint A; in rhix cá$e, P ir the p*int {*1.0}. If r = 3r/'?. rben p is the poinr
{*. -i }, and if ¡ -'' ?r¡" then Pis the point d . Il r > ?zr, then ir will takc more rha¡.}
or:e cuurplete ci¡cnit Erf the circle et t$ trarc the ¿¡rc áF_
. wlren Í { 0. eÉr3 trace the circle in a dackw,isedirectian" T}ere will he a sing}e
point P on the circle C such that the arc length measu red in the clock*'ise directñrn
frcm,¡{ is r' Thu*, for every reat number ¡. $scafl associate a *nique print p{a ,uJ
cn the unil circle.This allows us to make the kev definitions of rhe sine and cosíni
functit¡n*'The functi$ns riine a*{t eorine arewritlen as ¡¡in and cfi$. rathÉr tha* as a
single letter such as/org. Parentheses around the indepenrient variahle or* uroally
ornitted ünless rhere is sc¡me arnbiguitl,'.