Graphing Secant Cosecant Tangent Cotangent
Pre-Calculus Unit 5 – November 2nd to November 13th 2012Graphing & Writing Secant, Cosecant, Tangent and Cotangent FunctionsDateFri11/2Mon11/5Tues11/6Topic4.6 Graphing Secant and CosecantWed11/74.6 Writing Equations: Sec, Csc, Tan, OTES p.1 & 24.6 Graphing Tangent and CotangentNOTES p. 5Worksheet p. 3, 4 (#5 – 12)Worksheet p. 6, 7 (#3 – 10)Worksheet – in class (8 problems)HW – Study for quiz4.6 Graphing all 4: sec, csc, tan, cotNOTES p. 8QUIZ: Graphing sec, csc, tan, cot4.7 Inverse Trig FunctionsDid ItAssignmentWorksheet p. 8 & 9 (#5 – 12)NOTES p. 10 & 11Worksheet p. 11NOTES p. 12Worksheet p. 12Solving Equations: Calculator TrigReview Sheet – p. 13,14HW – Study for TestReview for Test – work on review in classTEST – Unit 5Print Unit 6 – Triangle TrigSinusoidal Regression PROJECT DUESecanty Parent equation:Domain: Period: Range: x Equation of Asymptotes: Two Specific Asymptotes:Cosecanty Parent equation: Domain:Period:Range: x Equation of Asymptotes: Two Specific Asymptotes:p. 1
TRANSFORMATIONS:SecantCosecantGeneral Equationy a sec b( c) dy a csc b( c) dPeriod2 b2 b To Find Domain and Asymptote Equationx 211.) y sec 3 2b Period: Phase Shift: n bx cn cb2.) y 2csc 1b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x Domain: Range: x Domain: Range: 3.) y sec( )2b Period: Phase Shift:4.) y csc 2( )2b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x Domain: Range: xDomain: Range:p. 2
PreCalculus – Worksheet – Graphing Secant and CosecantSketch the graph. Determine b, the period, phase shift, vertical shift, 2 specific asymptotes, the asym equation, domain and range.5.) y 2csc 26.) y sec 2 2b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x Domain: Range: Domain: Range: 8.) y sec( ) 237.) y 2sec( )6b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y xy x Domain: Range: Domain: Range:p. 3x
9.) y csc 2( 3110.) y sec 2)b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x Domain: Range: xDomain: Range:11.) y 3 csc 3 12.) y 2csc( ) 2b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x Domain: Range: Domain: Range:p. 4x
yNOTESTangent Parent equation: Domain:Range: Period: Equation of Asymptotes: x Two Specific Asymptotes: yCotangent Parent equation: Domain:Range: Period: Equation of Asymptotes: x Two Specific Asymptotes: TRANSFORMATIONS:Tangenty a tan b( c) dPeriod bCotangenty a cot b( c) dPeriod b 1.) y 2 tan 1Domain/Asymptotesx 2Domain/Asymptotoesx 2.) y cot 2( n b cn cb b Period: Phase Shift:)6b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:yy x Domain: Range: Domain: Range:p. 5x
PreCalculus – Worksheet – Graphing Tangent and CotangentSketch the graph. Determine b, the period, phase shift, vertical shift, 2 specific asymptotes, the asym equation, domain and range.b Period: Phase Shift:11cot 22b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y tan 3.)4.)y y y y tan ( Domain: Range:5.)x xDomain: Range:2 ) 236.) y 2cot b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:yy Domain: Range:x x Domain: Range:p. 6
7.)1 y tan ( )228.)y 2cot 2 2b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:yy x x Domain: Range:9.) Domain: Range: y 3tan( )610.)1y 2cot 12b Period: Phase Shift:b Period: Phase shift:V. Shift: 2 asym:V. Shift: 2 asym:Asymptote Eq:Asymptote Eq:y y x x Domain: Range: Domain: Range:p. 7
Writing Equations – Notes1) period asym:2) periodasym:a b a b c d c d Equation:3) period asym:Equation:4) periodasym:a b a b c d c d Equation:Equation:Writing Equations – Homework5) period asym:6) periodasym:a b a b c d c d Equation:Equation:More on page 9 p. 8
Writing Equations – Homework (cont’d)7) period asym:8) periodasym:a b a b c d c d Equation:9) period asym:Equation:10) periodasym:a b a b c d c d Equation:11) period asym:Equation:12) periodasym:a b a b c d c d Equation:Equation:p. 9
NOTES – Inverse Trig FunctionsSketch the sine, cosine and tangent curves below.sinecosinetangentAll three graphs are NOT one-to-one, so their domains must be restricted to find an inverse that IS a function.Definition of Inverse Trig Functions:FunctionDomainy arcsin x if and only if sin y x 1, 1 y arccos x if and only if cos y x 1, 1 y arctan x if and only if tan y x , Sketch:y arcsin x or y sin -1 xy arcos x or y cos -1 xRange 2 , 2 0, , 2 2 Reciprocals also haverestrictions on their range:csc 1 2 ,0 0, 2 sec 1 0, 2 2 , cot 1 0, y arctan x or y tan -1 xHaving restricted the interval on which we graph so that each inverse is a function results in only one answer for eachproblem. The range of sine and tangent is in Quadrants I and IV, while the range of cosine is Quadrants I and II.Label this information on a coordinate plane below.p.10
Evaluate the expression without using a calculator. Give your answer in radians. 1 3) sin 1 2 2 7) cos 1 2 3 11) arcsin 2 221) tan 1 12) arccos5) arcsin 16) csc 1 3 9) arctan 3 10) arccos ( 1)234) sec 1 2 8) cot 13312) csc 1 2Draw a reference triangle and evaluate each of the following expressions.113) sin arccos 2 617) sin csc 1 5 14)3 tan arcsin 5 118) cot tan 1 10 Homework – Inverse Trig Functions 115) cos arcsin 4 16) tan arccos19) sec cot 1 5 20) tan sec 1 12 5 6 13 3 (from Textbook section 4.7 p. 349 – 350 #1 – 16 and #49 – 58 )p.11
NOTES – Solving simple trig equations using a calculatorStep 1 – Determine the reference angle using the trig inverse buttons on your calculatorStep 2 – Determine where the angle could lie (Quad I, II, III, IV)Step 3 – Find both angle values of I.Determine the values of , where 0 360 , to the nearest hundredth of a degree. (calc. in DEGREE mode)1. sin .7183ref. angle: 2nd sin .7183 45.91 Sine is positive in Quadrants I and IIQuadrant I answer is 45.91Quadrant II answer is 180º – 45.91 134.094. sec – 4.80973. cos – .6691II. Determine the values of6. sin ( type 2nd cos (1/ 4.8097 ))2. tan 1.61985. cot – .1228 , where 0 2 , to the nearest hundredth of a radian. – .81837. tan 2.4567( type 2nd tan (1/ .1228))(calc. in RADIAN mode)8. csc – 1.1859HOMEWORK – Put work and answers on separate paper.I.Determine the values of , where 0 360 , to the nearest hundredth of a degree.1. sin 0.40672. cos – 0.50233. tan 2.99884. sec 1.11115. cot – 1.22226. csc 2.5012II.Determine the values of7. sin 10. csc 0.8143 1.0204 , where 0 2 , to the nearest hundredth of a radian.8. cos 0.783811. cot 0.58909. tan(Radian Mode) 12. sec –.2677 – 1.5861p.12
Graphing & Writing Secant, Cosecant, Tangent and Cotangent Functions Date Topic Assignment Did It Fri 11/2 4.6 Graphing Secant and Cosecant NOTES p.1 & 2 Worksheet p. 3, 4 (#5 – 12) Mon 11/5 4.6 Graphing Tangent and Cotangent NOTES p. 5 Worksheet p. 6, 7 (#3 – 10) Tues 11/
Cosecant, Secant & Cotangent mc-TY-cosecseccot-2009-1 In this unit we explain what is meant by the three trigonometric ratios cosecant, secant and cotangent. We see how they can appear in trigonometric identities and in the solution of trigonometrical equations. Finally, we obtain graphs of the functions cosecθ, secθ and cotθ
Cosecant, secant, and cotangent are periodic functions. Cosecant and se-cant have the same period as sine and cosine do, namely 2ˇ. Cotangent has period ˇ, just as tangent does. In terms of formulas, the previous two sentences mean that csc( 2ˇ) csc( ) sec( 2ˇ) sec( ) cot( ˇ) cot( )
becomes corresponding to secant i.e. cosecant. Cosecant with angle Ө secant (hypotenuse) / Opposite side (cotangent) cosec Ө AC / AB The defination of Cosecant : - it is the ratio of hypotenus i.e.secant to the opposite side of given triangle. The reason for main function sine , secant , tangent :- Sine is only use for chord which is .
Section 7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions. OBJECTIVE 1: Understanding the Graph of the Tangent Function and its Properties Recall that y tanx can equivalently be written y sin x cosx. Recall also that division by zero is never allowed. Therefore, the domain of
of cantilevered, braced, and/or anchored secant and tangent pile retaining wall systems. Secant and/or tangent pile walls may be constructed using various technologies including . A reinforced concrete template that is formed in the ground prior to the start of the construction of the secant or tangent pile walls. The guidewall provides .
So, the tangent function is a periodic function. Its period is . Lesson 6-7 Graphing Other Trigonometric Functions 395 6-7 R e a l W o r l d A p p lic a t i o n OBJECTIVES Graph tangent, cotangent, secant, and cosecant functions. W rite equations of trigonometric functions. midpoint d 6
Precalculus: Graphs of Tangent, Cotangent, Secant, and Cosecant The Cotangent Function The tangent function is cotx cosx sinx. It will have zeros where the cosine function has zeros, and vertical asymptotes where the sine function has zeros. It will look like the cosine function where the sine is essentially equal to 1, which is when xis near .
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