Pre-Calculus Unit 4- 1st 9-weeks



Pre-Calculus Unit 5- 2nd Term October 26th to November 7th 2011

Graphing & Writing Secant, Cosecant, Tangent and Cotangent Functions

|Date |Topic |Assignment |

|Wednesday |4.6 Graphing Secant and Cosecant |Worksheets 2 to 5 odds |

|10/26 |Notes page 1 and evens pages 2 to 5 | |

|Thursday |4.6 Graphing Tangent and Cotangent |  |

|10/27 |Notes page 6 and evens pages 7 to 9 |Worksheet 7 to 9 odds |

|Friday |4.6 Graphing all 4: sec, csc, tan, cot | Finish Worksheets |

|10/28 |Quiz : parent functions sec, csc, tan, cot |page 2 to 9 |

|Monday |4.6 Writing Equations: Secant, Cosecant, Tangent and Cotangent |Worksheet page 11 |

|10/31 |NOTES page 10 | |

|Tuesday |Quiz: Graphing Tangent and Cotangent |Finish problems page 13 |

|11/1 |Inverse Trig Functions Notes page 12 , 13 | |

|Wednesday |Inverse Trig Functions con’t. |Book p 349– 350 |

|11/2 | |1 -16, 43-58 |

|Thursday |Solving equations: Calculator Trig | |

|11/3 |Quiz: Inverse Functions Writing equations |Worksheet page 14 |

|Friday 11/4 |Review |Study |

|Monday11/7 |Test #5 |Print out Unit 6 |

Secant

Parent equation: ________________

Domain:____________ Period: ______

Range: ______________

Equation of Asymptotes:

Two Specific Asymptotes:

General Equation: _________________________

Domain:_________________ Range: ____________________ Period: ______

General Equation of Asymptotes: _____________________________

Cosecant

Parent equation: ________________

Domain:____________ Period: ______

Range: ______________

Equation of Asymptotes:

Two Specific Asymptotes:

General Equation: _________________________

Domain:_________________ Range: ____________________ Period: ______

General Equation of Asymptotes: _____________________________

page1

Sketch the graph of the function. Determine b, the period, phase shift, vertical shift. Find 2 Asymptotes, Domain and Range.

1. [pic] 2. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

3. [pic] 4. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: __________

page 2

5. [pic] 6. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: __________

7. [pic] 8. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

page 3

9. [pic] 10. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

11. [pic] 12. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

page 4

13. [pic] 14. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

15. [pic] 16. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

page 5

Tangent

Parent equation: ________________

Domain:_________________

Range: _____ Period: ______

Equation of Asymptotes:

Two Specific Asymptotes:

General Equation: _________________________

Domain:_________________ Range: _____ Period: ______

General Equation of Asymptotes: _____________________________

Cotangent

Parent equation: ________________

Domain:_________________

Range: _____ Period: ______

Equation of Asymptotes:

Two Specific Asymptotes:

General Equation: _________________________

Domain:_________________ Range: _____ Period: ______

General Equation of Asymptotes: _____________________________

page 6

Sketch the graph of the function. Determine b, the period, phase shift, vertical shift. Find 2 Asymptotes, Domain and Range.

1. [pic] 2. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

3. [pic] 4. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

page 7

5. [pic] 6. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

7. [pic] 8. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

9. [pic] 10. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________ page 8

11. [pic] 12. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

13. [pic] 14. [pic]

b = ________ Period: ________ b = _______ Period: _______

Phase Shift: _______ V. Shift: _______ Phase shift: _______ V. Shift: _______

Asymptotes: ______________________ Asymptotes: _________________________

`

Domain: ___________ Range: ___________ Domain: ___________ Range: ___________

page 9

Writing Equations – Notes

1) period _______ b_______ 2) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

3) period _______ b_______ 4) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

5) period _______ b_______ 6) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

page 10

Writing Equations - Homework

1) period _______ b_______ 2) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

3) period _______ b_______ 4) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

5) period _______ b_______ 6) period _______ b_______

a = _______ d = ______ c = ______ a = _______ d = ______ c = ______

asy: ___________________ asy: ___________________

equation: ________________ equation: ________________

page 11

Inverse Trig Functions

Sketch the sine, cosine and tangent curves below.

sine cosine tangent

All 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:

Function Domain Range

y = arcsin x if and only if sin y = x [pic] [pic]

y = arccos x if and only if cos y = x [pic] [pic]

y = arctan x if and only if tan y = x [pic] [pic][pic]

Sketch:

y = arcsin x or[pic] y = arcos x or [pic] y = arctan x or [pic]

Having restricted the interval on which we graph so that each inverse is a function results in only one answer for each problem. 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.

page 12

Inverse Trig Functions

Draw a reference triangle and evaluate each of the following expressions.

1) [pic] 2) [pic] 3) [pic] 4) [pic] 5)[pic]

6) [pic] 7) [pic] 8) [pic] 9) [pic] 10) [pic]

11) [pic] 12) [pic] 13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic] 18) [pic]

Inverse Functions of Special Angeles

Evaluate. Give your answers in radians.

1) a) [pic] 2) a) [pic] 3) a) [pic] 4) a) [pic]

b) [pic] b) [pic] b) [pic] b) [pic]

c) [pic] c) [pic] c) [pic] c) [pic]

5) a) [pic] 6) a) [pic] 7) a) [pic] 8) a) [pic]

b) [pic] b) [pic] b) [pic] b) [pic]

c) [pic] c) [pic] c) [pic] c) [pic] page 13

Calculator trig reference angles NOTES

I Determine the values of[pic], where [pic], to the nearest hundredth of a degree.

Determine the reference angle using your calculator. (Degree Mode) Where could the angle lie? Quadrant I, II, II, IV

Find both angle values of [pic].

1. sin [pic] = .7183 solution: 2nd sin .7183 = 45.91° 2. tan [pic] = 1.6198

Sine is positive in Quadrants I and II

Quadrant I answer is 45.91

Quadrant II answer is 180º – 45.91 = 134.09

3. cos[pic] = – .6691 4. sec[pic]= – 4.8097 (2nd cos 1/– 4.8097 ) 5. cot [pic] = – .1228 (2nd tan 1/– .1228)

II Determine the values of [pic], where [pic], to the nearest hundredth of a radian. (Radian Mode)

6. sin [pic] = – .8183 7. tan [pic] = 2.4567 8. csc [pic] = – 1.1859

HOMEWORK

I Determine the values of[pic], where [pic], to the nearest hundredth of a degree.

1. sin [pic] = 0.4067 2. cos [pic] = – 0.5023 3. tan [pic] = 2.9988

4. sec [pic] = 1.1111 5. cot [pic] = – 1.2222 6. csc [pic] = 2.5012

II Determine the values of [pic], where [pic], to the nearest hundredth of a radian. (Radian Mode)

7. sin [pic] = 0.8143 8. cos [pic] = 0.7838 9. tan [pic] = –.2677

10. csc [pic] = 1.0204 11. cot [pic] = 0.5890 12. sec [pic] = – 1.5861

page 14

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