Precalculus 2017-2018 Unit 3: Trig Fundamentals Plano Senior High School Topic 2: Trig Graphs & Transformations Subject to change

HW 6: Graph Sine, Cosine and Tangent 1) Graph 2 positive periods of y = cos x. 2) Graph one positive and one negative period of y = sin x.

3) Graph: y = tan x on the interval:

2

3,

2

4) State the range of the sine functions. 5) What is the domain of the cosine function? 6) State the vertical asymptotes of the tangent function.

7) For what values of x, 20 x , is the graph of xy sin increasing?

8) State the y-intercept of xy sin ? xy cos ? xy tan ?

9) Does the function have even, odd or neither type of

symmetry for xy sin ? xy cos ? xy tan ?

10) Where are the zeros of xy sin ? xy cos ? xy tan ?

11) What is the period of xy sin ? xy cos ? xy tan ?

HW 7: Graph Secant, Cosecant and Cotangent 1) Graph two periods of y = csc (x). 2) Graph one period y = sec (x)

3) Graph 0,2,cot)( xxf

4) State the y-intercept of y = sec(x)? y = csc(x)? y = cotx? 5) State the period of y = sec(x)? y = csc(x)? y = cotx? 6) Does the function have even, odd or neither type of

symmetry for y = sec(x)? y = csc(x)? y = cotx?

7) For what numbers x, 22 x , does csc(x) = -1?

8) Where does y = sec(x) have vertical asymptotes? 9) What are the zeros of y = cotx? 10) What is the range of the secant function? 11) What is the domain of the cosecant function?

12) Determine the quadrant in which the angle lies if

0sec and 0sin .

13-21 :List all of the six trig functions that… 13. …are continuous. 14. …have a domain of πkx

15. …have a range of , .

16. …are even. 17. …have a period of π2 . 18. …have amplitude.

19. …are periodic.

20. …go through 0,0

21. …have vertical asymptotes πk

πx

2

Monday Tuesday Wednesday Thursday Friday

January 15 16 17 18 19

Martin Luther King Jr. Day

Graph sine, Cosine, Tangent HW 6

Graph Secant, Cosecant, Cotangent HW 7

Transform Sine and Cosine HW 8

Transform Tangent & Cotangent HW 9

22 23 24 25 26

Write Equations from Graphs HW 10

Linear and Angular Velocity HW 11

Apply Sinusoids HW 12

Applications Day 2 Discretionary Day

29 30 31 February 1 2

Review

Trig Graphs & Transformations Test

HW 8: Transform Sine and Cosine Sketch one complete cycle. Label significant features and list Domain and Range.

1. y = 3 cos x 2. y = - sin 4x 3.

xy

2

1cos4 4. xy 2cos

3

1

5. xy πsin 6.

xy

3

1sin5 7. xy sin5 8. 4

2sin2

xy

9. 122

cos3

xy

10.

)3(

3

1cos3 xy 11. 3)

2(2sin

xy 12. xy 2cos45

HW 9: Transform Tangent and Cotangent Graph one period. Write the domain and range.

1) xtan4y 2) 3)xtan(y 3) )xtan(5y 4) 4)tan(2 xy

5)

x

4

1tany 6) 2x

2

1tan3y

7) 3)x4tan(y 8) )x5tan(4y

9) x2coty

10). 4xπcoty 11) 1xcot4y 12)

8

πx2cot3y

HW 10: Write Equations from Graphs Write an equation of a sinusoidal function with the given characteristics or a graph.

1. A transformation of xy cos with these characteristics:

amplitude of 3, phase shift of2

, period of π, shift up 3.

2. A transformation of xy sin with these characteristics:

amplitude of 5, phase shift of -1, period of 1.

3. 4. 5. 6. 7. 8.

-2 -1 1 2 3 4 5 6 7 8 9 10

0.1

0.2

0.3

0.4

0.5

-8 -6 -4 -2 2 4 6 8

-1

1

2

-8 -6 -4 -2 2 4 6

-8

-6

-4

-2

-10 -8 -6 -4 -2 2 4 6 8 10

-1

1

2

3

4

5

6

HW 11: Linear and Angular Velocity

Complete these book problems: P 238: 35-37, 39,

HW 12: Apply Sinusoids 1. As you ride the Texas Star Ferris wheel at the State Fair of Texas, your distance from the ground varies sinusoidally

with time. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes you 30 seconds to reach the top, 212 feet above the ground, and that the wheel makes a revolution once every 80 seconds. The diameter of the wheel is 200 feet.

a) Write an equation for this sinusoid. b) Predict your height above the ground when

(i) t = 0, (ii) t = 50, (iii) t = 70, (iv) t = 110. c) When is the 3rd time you will be 150 ft high? 2. Betty Lou was sitting on the front porch of her plantation when the riverboat went by. As the paddlewheel turned, a

point on the paddle blade moved in such a way that its distance, d from the water's surface was a sinusoidal function of time. Four seconds later, the point was at its highest, 16 feet above the water's surface. The diameter of the wheel was 18 feet, and it completed a revolution every 10 seconds.

a) Sketch one period of the graph. b) Write the equation of the sinusoid.

c) How far above the surface was the point after (i) 5 seconds, (ii) 17 seconds?

3. Researchers find a creature from an alien planet. Its body temperature is varying sinusoidally with time. 32 minutes

after they start timing, it reaches a high of 124 F. 26 minutes after that it reaches its next low, 102 F. a) Sketch one period of this sinusoid. b) Write an equation expressing the temperature in terms of the number of minutes since they started timing.

c) What was its temperature when they first started timing? 4. The average daily temperature in Dallas is measured monthly. It reaches a low of 44.6°F in January and a high of 85.8°F in July. Assume that the average daily temperature varies sinusoidally throughout the year.

a) Sketch a graph of this function. b) Write an equation of this function. 5. As an oil well like the one shown pumps, the height of its cathead varies sinusoidally with time. Suppose that the

pump is started at time t = 0 sec. Two seconds later, it is at its highest point above the ground, 22 ft. It is at its next low point (8 ft) 2.5 seconds after that.

a) Sketch a graph of this function. b) Write an equation for this function.

ANSWERS HW 6 ANSWERS: 1) y = cos x 4,0 2 ) y = sin x 2,2 3)

4) 1,1 5) All reals 6) k2

7)

2,0 U

2,

2

3

8) Sine has a y intercept of 0, cosine has a y intercept of 1, tangent has a y intercept of 0 9) Sine is odd, cosine is even, tangent is odd

10) Sine has zeroes at kx , cosine has zeroes at k2

x

, tangent has zeroes at kx

11) Sine has a period of 2 , cosine has a period of 2 , tangent has a period of . HW 7 ANSWERS: 1. xy csc 2. xy sec 3. y = cot x

4. Secant has a y-intercept of 1, Cosecant does not have a y-intercept, Cotangent does not have a y- intercept

5. Secant has a period of 2 , Cosecant has a period of 2 , Cotangent has a period of . 6. Secant is even, Cosecant is odd, and Cotangent is odd.

7. 2

3&

2

8. kx

2 9. kx

2 10. ),1[]1,(: R

11. kx 12. II 13. Sine and Cosine 14. Cosecant and Cotangent 15. Tangent and Cotangent 16. Cosine and Secant 17. Sine, Cosine, Secant, and Cosecant 18. Sine and Cosine 19. All 20. Sine and Tangent 21. Secant and Tangent

x

y

x

y

x

y

x

x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

y

HW 8 ANSWERS: 1. 2.

3. 4.

5. 6.

7. 8.

D: (-∞, ∞) R: [-3, 3] D: (-∞, ∞) R: [-1, 1]

D: (-∞, ∞) R: [-4, 4] D: (-∞, ∞) R: [-0.3, 0.3]

D: (-∞, ∞) R: [-1, 1] D: (-∞, ∞) R: [-5, 5]

D: (-∞, ∞) R: [4, 6] D: (-∞, ∞) R: [2, 6]

x

y

x

y

x

y

x

y

9. 10.

11. 12.

HW 9 ANSWERS:

1. 2. 3.

D: k2

x

R: ),( D: k2

x

R: ),( D: k2

x

R: ),(

4. 5. 6.

D: k2

x

R: ),( D: k42x R: ),( D: k2x R: ),(

x

y

x

y

x

y

x

y

x

y

x

y

D: (-∞, ∞) R: [-2, 4] D: (-∞, ∞) R: [-3, 3]

D: (-∞, ∞) R: [-4, -2] D: (-∞, ∞) R: [1, 9]

7. 8.

D: k48

x

R: ),( D: k510

x

R: ),(

9. 10.

D: k2

πx R: ),( D: kx R: ),(

11. 12.

D: kπx R: ),( D: k2

π

8

π3x R: ),(

HW 10 ANSWERS:

x

y

x

y

p/8 p/4 3p/8 p/2

y = -cot(2x)

0.5 1.0

123456789y = cot(pi*x)+4

x

y

p/2 p

2

4

6

8

y = 4 cot(x) - 1

x

y

-p/8 p/8 p/4 3p/8

-14

-12

-10

-8

-6

-4

-2

2

4

6

8

10

12

14y = 3cot(2(x + pi/8))

16

-2

7

4 149

58

-2

32

4 14

84

113102

124

4.5 7

8

22

21 7 13

20.6

85.8

1. 32

2cos3

xy 2. 1xπ2sin5y 3. 25.14

cos05. xy

4. 42

1

2cos3

xy

5. 12

1cos3

xy 6. 1)1(

4cos

2

1 xy

7. 2)1(

4cos3 xy

8. 3)100(

800cos7 xy

HW 11 ANSWERS: 35) 1.125 rev/min 36) 52 rev/min 37) r=5.999 m 39) 16.3 in

HW 12 ANSWERS:

1) a) y = 100 112))30(40

cos( x

b) (i) t = 0, h = 41.289 ft (ii) t = 50, h = 112 ft

(iii) t = 70, h = 12 ft (iv) t = 110, h = 212 ft

c) 94.963 secs

2) a) 3) a)

b) b) 113)32(26

cos11

xy

c) i) 14.281 ft ii) 4.219 ft c) 104.766

4) a) 5) a)

b) 2.65)1(6

cos6.20

xy

b) 15)2(

5

2cos7

ty

7)4(5

cos9

td

44.6