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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