F.TF.B.5: Modeling Trigonometric Functions 1a

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



F.TF.B.5: Modeling Trigonometric Functions 1a

1 The equation y - 2 sin = 3 may be rewritten as 1) f(y) = 2 sinx + 3 2) f(y) = 2sin + 3 3) f(x) = 2sin + 3 4) f() = 2sin + 3

2 The voltage used by most households can be modeled by a sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds? 1) V = 120sin(t) 2) V = 120sin(60t) 3) V = 120sin(60t) 4) V = 120sin(120t)

3 Which equation is represented by the graph below?

Name: ________________________ 4 Which equation represents the graph below?

1) y = -2sin 2x

2)

y=

-2

sin

1 2

x

3) y = -2 cos 2x

4)

y=

-2 cos

1 2

x

5 The accompanying diagram shows a section of a sound wave as displayed on an oscilloscope.

1) y = 2 cos 3x

2) y = 2 sin3x

3)

y

=

2

cos

2 3

x

4)

y

=

2 sin

2 3

x

Which equation could represent this graph?

1)

y

=

2 cos

x 2

2)

y

=

2 sin

x 2

3)

y

=

1 2

cos

x 2

4)

y

=

1 2

sin

2

x

1

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



6 A radio transmitter sends a radio wave from the top of a 50-foot tower. The wave is represented by the accompanying graph.

Name: ________________________

8 Which equation is represented by the graph shown below?

What is the equation of this radio wave? 1) y = sinx 2) y = 1.5sinx 3) y = sin 1.5x 4) y = 2sinx

7 Which equation is represented by the accompanying graph?

1)

y

=

1 2

cos 2x

2) y = cos x

3)

y

=

1 2

cos x

4)

y

=

2 cos

1 2

x

9 Which equation is represented by the accompanying graph?

1) y = cos x

2)

y

=

cos

1 2

x

3) y = cos 2x

4)

y

=

1 2

cos x

1)

y

=

2 sin

1 2

x

2) y = 2sinx

3)

y

=

sin

1 2

x

4) y = sin2x

2

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



10 Which is an equation of the graph shown below?

Name: ________________________

12 Which equation is represented by the graph in the diagram below?

1) y = sin2x 2) y = -sin2x 3) y = -2 sinx 4) y = 2sinx

11 Which is an equation of the graph shown below?

1) y = 3 sin2x

2)

y

=

3 sin

1 2

x

3) y = -3sin 3x

4)

y=

-3

sin

1 2

x

13 Which equation is represented by the graph below?

1)

y

=

cos

1 2

x

2) y = cos 2x

3)

y

=

sin

1 2

x

4) y = sin2x

1)

y=

-2

sin

1 2

x

2)

y=

-

1 2

sin

2x

3)

y

=

1 2

sin 2x

4)

y

=

2 sin

1 2

x

3

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



14 Which equation is represented in the graph below?

Name: ________________________

16 Which equation is represented by the graph in the accompanying diagram?

1) y = 2 cos 2x

2)

y

=

1 2

cos 2x

3)

y

=

2 cos

1 2

x

4)

y

=

1 2

cos

1 2

x

15 Which equation is represented in the accompanying graph?

1) y = 3 sin2x 2) y = 2 sin3x 3) y = 3sinx 4) y = 2 sin4x

17 Which trigonometric function is shown in the graph below?

1) y = 2 sin2x

2)

y

=

1 2

sin

1 2

x

3)

y

=

2 sin

1 2

x

4)

y

=

1 2

sin 2x

1) f(x) = 2sinx 2) f(x) = 2cos x 3) f(x) = cos 2x 4) f(x) = sin2x

4

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



18 Which equation is represented by the graph in the accompanying diagram?

Name: ________________________

20 Which equation could be represented by the graph below?

1) y = 3 sin2x

2)

y

=

3 sin

1 2

x

3) y = 2 sin3x

4)

y

=

1 2

sin 3x

19 Which equation is represented on the graph shown below?

1)

y

=

2 sin

1 2

x

2)

y

=

2 cos

1 2

x

3)

y

=

1 2

sin 2x

4)

y

=

1 2

cos 2x

1) y = 3sinx 2) y = -3 sinx 3) y = 3 cos x 4) y = -sin3x

5

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



21 In physics class, Eva noticed the pattern shown in the accompanying diagram on an oscilloscope.

Name: ________________________

23 The function f(x) = a cos bx + c is plotted on the graph shown below.

Which equation best represents the pattern shown

on this oscilloscope?

1)

y

=

sin

1 2

x

+

1

2) y = sin x + 1

3) y = 2sinx + 1

4)

y

=

2

sin

-

1 2

x

+

1

22 The accompanying graph represents a portion of a sound wave.

What are the values of a, b, and c?

1) a = 2, b = 6, c = 3

2) a = 2, b = 3, c = 1

3) a = 4, b = 6, c = 5

4)

a

=

4,

b

=

3

,

c

=

3

24 Which equation is graphed in the diagram below?

Which equation best represents this graph?

1)

y

=

2 sin

1 2

x

2)

y

=

sin

1 2

x

+

2

3) y = sin2x

4) y = sin2x + 2

1)

y

=

3

cos

30

x

+

8

2)

y

=

3

cos

15

x

+

5

3)

y

=

-3

cos

30

x

+

8

4)

y

=

-3

cos

15

x

+

5

6

Regents Exam Questions F.TF.B.5: Modeling Trigonometric Functions 1a



25 The depth of the water at a marker 20 feet from the shore in a bay is depicted in the graph below.

Name: ________________________ 26 Which equation is represented by the graph below?

If the depth, d, is measured in feet and time, t, is

measured in hours since midnight, what is an

equation for the depth of the water at the marker?

1)

d

=

5 cos

6

t

+

9

2)

d

=

9 cos

6

t

+

5

3)

d

=

9 sin

6

t

+5

4)

d

=

5 sin

6

t

+9

1) y = cot x 2) y = csc x 3) y = sec x 4) y = tanx

27 Which equation is sketched in the diagram below?

1) y = csc x 2) y = sec x 3) y = cot x 4) y = tanx

7

ID: A

F.TF.B.5: Modeling Trigonometric Functions 1a Answer Section

1 ANS: 4 y - 2sin = 3

y = 2sin + 3

f() = 2sin + 3

REF: fall0927a2

2 ANS: 4

period =

2 B

1 60

=

2 B

B = 120

REF: 061624aii

3 ANS: 1

REF: 011320a2

4 ANS: 3

REF: 061306a2

5 ANS: 1

Since none of the answers has a translation, the point (0,2) must result from a dilation of 2 of the cosine function.

At x = , the function is complete, so the period is 4.

.

REF: 010214b 6 ANS: 2

The maximum and minimum of this sine function indicates the amplitude is 1.5.

REF: 060608b 7 ANS: 1 8 ANS: 1 9 ANS: 1 10 ANS: 3 11 ANS: 1 12 ANS: 4 13 ANS: 1

REF: 060711b REF: 061708aii REF: 010419siii REF: 068633siii REF: 018917siii REF: 089522siii REF: 069721siii

1

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