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Solutions
16 Videos

Sketch the graph of a sinusoidal function that has a period of 6, an amplitude of 4, and whose equation of the axis is `y = -2`

.

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0.41mins

Q3

Coline is on a unique Ferris wheel: it is situated on the top of a building. Colin's height above the ground at various times is recorded in the table.

a) What is the period of the function, and what does it represent in this situation?

b) What is the equation of the axis, and What does it represent in this situation?

c) What is the amplitude of the function, and what does it represent in this situation?

d) Was the Ferris wheel already in motion when the data were recorded? Explain.

e) How fast is Colin travelling around the wheel, in metres per second?

f) What is the range of the function?

g) If the building is 6 m tall, what was Colin’s boarding height in terms of the building?

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Q4

a. Graph the function `f(x) = 4 \cos( 3x) + 9`

without using a graphing device.

b. Is the function sinusoidal?

c. Calculate `f(45)`

.

d. Determine the values of `x, 0^o \leq x \leq 360^o`

, for which `f(x) = 5`

.

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4.15mins

Q5

A ship is docked in port and rises and falls with the waves. The function d(t) = 2 sin(30t)° + 5 models the depth of the propeller, `d(t)`

, in metres at t seconds. Graph the function using a graphing calculator,and answer the following questions.

a. What is the period of the function, and what does it represent in this situation?

b. If there were no waves, what would be the depth of the propeller?

c. What is the depth of the propeller at t = 5.5 5?

d. What is the range of the function?

e. Within the first 10 s, at what times is the propeller at a depth of 3 m?

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3.36mins

Q6

Determine the coordinates of the image point after a rotation of 25° about (0, 0) from the point (4, 0).

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1.11mins

Q7

The sinusoidal function has undergone one transformation that may have affected the period, amplitude, or equation of the axis of the function. Determine which characteristic has been changed. If one has, indicate its new value.

```
\displaystyle
y = \sin x - 3
```

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0.32mins

Q8a

The sinusoidal function has undergone one transformation that may have affected the period, amplitude, or equation of the axis of the function. Determine which characteristic has been changed. If one has, indicate its new value.

```
\displaystyle
y = \sin(4x)
```

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0.25mins

Q8b

The sinusoidal function has undergone one transformation that may have affected the period, amplitude, or equation of the axis of the function. Determine which characteristic has been changed. If one has, indicate its new value.

```
\displaystyle
y = 7\cos(x)
```

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0.20mins

Q8c

```
\displaystyle
y = \cos(x - 70^o)
```

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0.58mins

Q8d

Use transformations to graph each function for `0^o \leq x \leq 360^o`

.

```
\displaystyle
y = 5\cos(2x) + 7
```

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1.10mins

Q9a

Use transformations to graph each function for `0^o \leq x \leq 360^o`

.

```
\displaystyle
y = -0.5\sin(x - 30^o) -4
```

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2.29mins

Q9b

Determine the range of each sinusoidal function without graphing.

```
\displaystyle
y = -3\sin(4x) +2
```

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0.29mins

Q10a

Determine the range of each sinusoidal function without graphing.

```
\displaystyle
y = 0.5\cos(3(x - 40^o))
```

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0.32mins

Q10b

Determine the sine function `y = a\sin k(\theta -d) + c`

for the graph.

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1.44mins

Q12a

Determine the sine function `y = a\sin k(\theta -d) + c`

for the graph.

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1.06mins

Q12b

Min is sitting in a rocking chair. The distance, `d(t)`

, between the wall and the rear of the chair varies sinusoidally with time `t`

. At `t = 1`

s, the chair is closest to the wall and `d(1) = 18`

cm. At `t = 1.75`

s, the chair is farthest from the wall and `d(1.75) = 34cm`

a. What is the period of the function, and What does it represent in this situation?

b. How far is the chair from the wall when no one is rocking in it?

c. If Meagan rocks back and forth `40`

times only, what is the domain of the function?

d. What is the range of the function in part (c)?

e. What is the amplitude of the function, and what does it represent in this situation?

f. What is the equation of the sinusoidal function?

g. What is the distance between the wall and the chair at `t = 8`

s?

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5.14mins

Q13