Tachr: CORE TRIGONOMETRY Yar: 2012-13 Cours: TRIGONOMETRY Month: All Months S p t m b r Angls Essntial Qustions Can I idntify draw ngativ positiv angls in stard position? Do I hav a working knowldg of Basic Trigonomtry vocabulary? Can I dscrib th rlationship btwn angl masurs in dgrs radians? Contnt Skills Assssmnts Lssons Trms - initial sid, trminal sid, positiv/ngativ, stard position Angl Masurmnt in Dgrs Quadrantal Angls Cotrminal Angls Trigonomtric Functions Idntify, classify, apply proprtis of ngativ positiv angls. Convrt angl masurs from dgrs to radians. Angl Writ Masurmnt in angl Radians: masurs dfining, in dgrs, convrting to minuts, from, arc lngth sconds. Quizzs 9/1/2012 Homwork 9/1/2012 Tachr Obsrvation Qustioning 9/1/2012 Larning Bnchmarks Stards Studnts will undrst b abl to us trig vocabulary. 12.M.01- Masurmnt ~ Dscrib th rlationship btwn dgr radian masurs, us radian masur in th solution of problms, in particular, problms involving angular vlocity acclration. 12.M.02- Masurmnt ~ Us dimnsional analysis for unit convrsion to confirm that xprssions quations mak sns.
Essntial Qustions Can I dfin th 6 functions in trms of x, y, r? Can I idntify us rfrnc angls? Can I apply th corrct sign valu for ach trig function in ach Quadrant? Right Triangls Contnt Skills Assssmnts Lssons Sign valu for ach trig functions in ach quadrant. Scant, Coscant, Cotangnt Dfin apply th rciprocal functions, sc, csc, cot. Dfin th 6 trig functions in trms of x, y, r. Dfin us rfrnc triangls to crat a rfrnc triangls. Apply th appropriat sign valu for ach trig function in ach quadrant. Quizzs Homwork Tachr Obsrvation Qustioning Tsts Larning Bnchmarks Stards Studnt will undrst hav a working knowldg of basic trig functions. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt of an acut angl. Apply to th solution of problms. 12.G.03- Gomtry ~ Us th notion of vctors to solv problms. Dscrib addition of vctors multiplication of a vctor by a scalar, both symbolically gomtrically. Us vctor mthods to obtain gomtric rsults. Essntial Qustions Can I us a varity of tchniqus to solv for triangls? Contnt Skills Assssmnts Lssons Pythagoran Thorm Spcial Right Triangls Right Apply th Pythagoran Thorm to solv for th lngths of a sid of a Quizzs 10/4/2012 Homwork 10/4/2012 Tachr obsrvation Larning Bnchmarks Stards Studnts will b abl to us trig to solv right triangls. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt
Am I abl to apply th basic functions? Triangl Trigonomtry: Sin, Cos,Tan right triangl. Apply proprtis of spcial right triangls to Application of Right Can I dscrib Triangl solv convy an Trigonomtry; triangls. undrsting angls of of th Basic lvation Trigonomtric dprssion Functions? Find valus of functions using a calculator. qustioning. 10/4/2012 Studnts of an acut will b abl angl. to apply trig Apply to to solv th solution ral-world of problms. problms. Us trig functions solv for angls sid lngths of right triangls. Us trig functions to solv ral world application problms. O c t o b r Non-Right Triangls Essntial Qustions Can I us a varity of tchniqus to solv for triangls? Can I apply th functions? Contnt Skills Assssmnts Lssons Law of Sins Cosins Ara of Triangls Hron's Formula Idntify apply th Law of Sins Cosins to solv problms. Find th ara of a triangl Quizzs Homwork Tachr Obsrvation Qustioning Larning Bnchmarks Stards Studnts will b abl to us a varity of tchniqus to solv, to find th ara of, triangls. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt of an acut angl. Apply to th solution of
N o v m b r Graphing Essntial Qustions Can I analyz th graphs of functions? Vctors using k=1/2absinc. Us apply Hron's formula. Contnt Skills Assssmnts Lssons Graphs of Sin Cosin Trms; Amplitud, Vrtical Shift, Priod, Phas Shift Introduc tangnt graphs. Idntify classify graphs of sin cosin. Crat graphs of sin cosin givn th quation or othr ssntial information. Idntify th amplitud, Priod, Shifts of a graph. Quizzs 12/31/2012 Homwork 12/31/2012 Tachr obsrvation qustioning 12/31/2012 problms. 12.G.02- Gomtry ~ Driv apply basic idntitis (.g., sin2q + cos2q = 1, tan2q + 1 = sc2q) th laws of sins cosins. Larning Bnchmarks Stards Studnts will b abl to analyz graph trig functions. 12.G.04- Gomtry ~ Rlat gomtric algbraic rprsntations of lins, simpl curvs, conic sctions. 12.P.13- Rlations Algbra ~ Dscrib th translations scal changs of a givn function Æ (x) rsulting from substitutions for th various paramtrs a, b, c, d in y = aæ (b(x +
D c m b r Idntitis Essntial Qustions Can I idntify Trigonomtric, Rciprocal, Pythagoran Idntitis? Can I apply th proprtis of Idntitis to solv problms? Can I prov Basic Idntitis c/b)) + d. In particular, dscrib th ffct of such changs on polynomial, rational, xponntial, logarithmic, functions. Contnt Skills Assssmnts Lssons Larning Bnchmarks Stards Trigonomtric, Dfin Rciprocal, Idntify th Pythagoran Idntitis. Proofs of Basic Idntitis. Trigonomtric, Rciprocal, Pythagoran Idntitis. Manipulat idntitis to solv problms. Prov Basic Idntitis. Quizzs Unit Tst Homwork Studnts will b abl 12.G.02- to prov Gomtry ~ basic trig Driv idntitis apply basic will us idntitis to idntitis solv trig (.g., sin2q + quations. cos2q = 1, tan2q + 1 = sc2q) th laws of sins cosins. 12.P.04- Rlations Algbra ~ Dmonstrat an undrsting of th, xponntial, logarithmic functions.
12.P.05- Rlations Algbra ~ Prform oprations on functions, including composition. Find invrss of functions. 12.P.08- Rlations Algbra ~ Solv a varity of quations inqualitis using algbraic, graphical, numrical mthods, including th quadratic formula; us tchnology whr appropriat. Includ polynomial, xponntial, logarithmic, functions; xprssions involving absolut valus; rlations; simpl rational
Trigonomtric Equations Essntial Qustions Can I apply Basic Trig Idntitis to solv quations? Am I abl to dmonstrat a varity of mthods usd to solv trig quations? Contnt Skills Assssmnts Lssons Trig Equations with Basic Idntitis Solving Trig Equations using Algbra Graphing Quizzs Homwork Final Exam xprssions. Larning Bnchmarks Stards Studnts will b abl to solv trig quations. 12.P.04- Rlations Algbra ~ Dmonstrat an undrsting of th, xponntial, logarithmic functions. 12.P.05- Rlations Algbra ~ Prform oprations on functions, including composition. Find invrss of functions. 12.P.06- Rlations Algbra ~ Givn algbraic, numric /or graphical rprsntations, rcogniz functions as polynomial, rational, logarithmic, xponntial, or. 12.P.08-
Rlations Algbra ~ Solv a varity of quations inqualitis using algbraic, graphical, numrical mthods, including th quadratic formula; us tchnology whr appropriat. Includ polynomial, xponntial, logarithmic, functions; xprssions involving absolut valus; rlations; simpl rational xprssions. 12.P.11- Rlations Algbra ~ Solv vryday problms that can b modld using polynomial, rational, xponntial, logarithmic,, stp functions,
J a n u a r y Rviw Essntial Qustions Can I solv both right nonright triangls? Do I undrst th bhavior of th trig functions? Am I abl to apply trig idntitis to simplify xprssions to solv quations? Contnt Skills Assssmnts Lssons absolut valus, squar roots. Apply appropriat graphical, tabular, or symbolic mthods to th solution. Includ growth dcay; joint (.g., I = Prt, y = k(w1 + w2)) combind (F = G(m1m2)/d2) variation, priodic procsss. Larning Bnchmarks Stards Can th studnt solv both right nonright triangls? Can th studnt apply trig idntitis to simplify xprssions solv quations? Can th studnt solv ral-world applications, scinc in particular?
Am I abl to tak a problm rcogniz whn which mthods of trig ar ncssary? Can th studnt solv ral-world applications, scinc in particular? Can I analyz intrprt graphs?