Graphing Trig And Verse Trig Functions - Weebly

Mon., Nov. 5thTest over Sine and Cosine andApplicationsTue., Nov 6thGraphing Secant, Cosecant, Tangentand Cotangent FunctionsBook reference Sec 4.6 p. 332Assignment Day 1 GraphingWed., Nov 7thGraphing OthersDay 2 Graphing plus AsymptoteworksheetThurs., Nov 8thWriting Equations and GraphingWriting Worksheet # 1 & 2Fri., Nov 9thQUIZ over Other GraphingBegin Graphing Inverse Trig FunctionsAssignment Graphing InverseMon., Nov 12thInverse Angles and Values Day 1Packet plus text p. 350 # 59-64Tue., Nov 13thInverse Values and Angles Day 2WorksheetWed., Nov 14thQUIZThurs., Nov 15thReview GameStudy for TestFri., Nov 16thTest over 4.3,4.6,4.7No HomeworkSec 4.3 in textAssignment Packet p. 17plus review1

GRAPHING ALL SIX TRIG FUNCTIONSy cosBasicshapeDomain Rangey secBasic shapeDomainRangeEquation ofasymptotesTwo specific asymptotesy tanBasic shapeDomainRangeEquation of asymptotesTwo specific asymptotes2

y sinBasic shapeDomain Rangey cscBasic shapeDomainRangeEquation ofasymptotesTwo specificasymptotesy cotBasic shapeDomainRangeEquation ofasymptotesTwo specific asymptotes3

Day 11)GRAPHINGytan x2DomainRangeEquation of asymptotesTwo specific asymptotes2)ycot4DomainRangeEquation of asymptotesTwo specific asymptotes3)y2secDomainRangeEquation of asymptotesTwo specific asymptotes4) y1csc x21DomainRangeEquation of asymptotesTwo specific asymptotes4

5)y3sec x16DomainRangeEquation of asymptotesTwo specific asymptotes6)ycsc 323DomainRangeEquation of asymptotesTwo specific asymptotes7)y2 tan 2x 3DomainRangeEquation of asymptotesTwo specific asymptotes8) ycot122DomainRangeEquation of asymptotesTwo specific asymptotes5

PRECALCULUSTRIG EQUATIONS AND THEIR ASYMPTOTESMatch the equation with its asymptotes.EquationAsymptotes1.y ½tan x 3A.2.y 2sec xB.3.y csc 2x - 4C.4.y tan x 2D.k25.y sec ½x 4E.π 2k6.y -3cotx – 2F.2kπ7.y cot (x -8.y sec ½ x9.y csc (2x -10.y tan (x 11.y sec (x -12.y tan (2x 13.y -4 tan ½x 314.y csc ½x 315.y cot(x -16.)22G.kπ2 k44k2k))2)22))4y 5sec(2x ) 16

Graphing Trig FunctionsDay 1Find the period, domain and range of each function. Find the general equation of the asymptotes and twospecific asymptotes on all sec ,csc , tan , and cot functions.1)ytan x2)y4)ycsc x5)y3sec x7)y2 tan 2x 38)ycot10)y2csc 2x 111)y3cot x21cot416122613)y sec6)y9)y12)ycsc 3321sec 2 x223tan x261Day 2Graphing Others Day 2Graph one cycle of each function.141. y tan xy2.3sec x3.2ycsc3x 14Graph and state whether each function is odd, even or neither.y tan x4.5.2y cot(x) 2If F is any function with period 5, determine the period of each related function. Provide a reason for youranswer.6.y F(x 1)7.y F(x) 5y8.F1x29.y F(3x)Graph one cycle of each function.10. y tan 2x43111.y3csc 2x431GRAPHING INVERSE TRIG FUNCTIONSFind the domain, range, and sketch a complete graph of each function. Inverse functions are denoted byysin1x or by yA rcsin x .1)y sin –1(3x)2)y cos–1(x) -5)y 3 arccos(2x-4)6)y tan –1(x-1) 8)y 3 cos–1 (x-2)9)y -21tan–1 (x-1)43)y arc sin (x 1)7)y – arc sin x 10)4)y 2 sin–1(x)32y cot–1 x 17

Writing Trig Equations WS #11)2)3)4)5)6)7)8)8

Writing Trig Equations WS #21)2)3)4)5)6)7)8)9

Graph one cycle and fill in the blanks.11. yPeriod sec 2 x122Equation of AsymptotesThree Specific Asymptotes2. y3cot x61Period Equation of AsymptotesTwo Specific Asymptotes3. yPeriod 2csc 2x 1Equation of AsymptotesThree Specific Asymptotes10

4. y3tan x26Period Equation of AsymptotesTwo Specific AsymptotesWrite the equation for each graph.5.Equation:6.Equation:11

Evaluate.27. cos38. tan10. cot2313. cos55sinsincos646414. cos37cos46549. sin5612. sec311. cscsin5337sin4673415.71 tan tan34tantanIf 0in radians that make each statement true.2 , determine the values of316. cos17. tan18. csc32219. cot 21320. sec24321. csc2212

Notes on graphing inverses of sine and cosine graphs1st Graph y sin x2 nd Interchange the values in the ordered pair and sketch inthe graph below:anglevalueangle3rd graph yvalueSin 1 ( x)anglevaluePart 2 ) Do the same as above but to the graph y cosine x1st Graph y cos x2 nd Interchange the values in the ordered pair and sketch in the graph below:anglevalueangle3rd graph yCos 1 ( x )valueanglevalue13

1st2 nd Interchange the values in the ordered pair and sketch in the graph below:Graph y tan xanglevalueangle3rd graph ytan 1 ( x)valueanglevaluePart 2 ) Do the same as above but to the graph y cosine x1st Graph y cot x2 nd Interchange the values in the ordered pair and sketch in the graph below:anglevalueangle3rd graph yCot 1 ( x)valueanglevalue14

INVERSE TRIG FUNCTIONS PROBLEMS NOTESTWO GROUPS BASED ON SIMILAR RANGEy sin 1 x[y tan 1 x(y csc 1 x[2, 22]2, 2)2, 2] , y 02Sample Problems35Reference Triangles3ex 1 sin(arctan( )2cot(sin 1 (10))10sec(arc tan 3x)Angle Problems4sin 1 (3)25arc tan(-1)6arcsin(tan3)4SECOND GROUPycos 1 x[0, ]ysec 1 x[0, ]ycot 1 x(0, )y2015

Sample ProblemsReference Triangles335ex 1 sin(arccos( ) )2sin(cos 1 (10))10sec(arc csc 3x)Angle Problems4cos 1 (3)25arc cot(-1)6arcsin(cos3)4Summary of quadrant locations for inverse functions.16

Examples:Find the exact values without using a calculator.1.sin11 3.sin1125.tan17.Arc csc 2 9.sec12.4.cos3 211 2A rccos6.csc1238.sec12 10.A rc cot1 31 212.A rcsin sin76 14.sin3 2 Find the exact value:11.sin A rccos13.Arc sec sec15.sin cos134 16.cos A rcsin17.tan sin112 18.sin tan 1( 1) 19.cos cot1 20.cos A rcsin21.sin Arc cos3 422.csc cos23.Arccot(-1) 24.cot412511sin 41 27 51329 3 17

Graphing Trig Functions Day 1 Find the period, domain and range of each function. Find the general equation of the asymptotes and two specific asymptotes on all sec ,csc , tan , and cot functions. 1) tan 2 yx 2) cot 4 y 3) y sec 4) yxcsc 1 5) 3sec 1 6 yx 6) csc 3 3 2 y 7) yx2tan2 3 8) 1 cot