chapter 6 assignment - sinusoidal function
knowledge and understanding /10, communication /10, thinking /10, application /10, total /40
multiple choice knowledge and understanding 10 marks--1 mark each
identify the choice that best completes the statement or answers the question. use only capital letters.
1. what are the peaks of a periodic function?
a. the extremes of the graph c. the highest points of the graph
b. the lowest points of the graph d. the x-intercepts of the graph
2. what is the amplitude of the function?
graph of a sinusoidal function with x-axis from -5 to 5 and y-axis from -7 to 7
a. 7 c. 10
b. 14 d. 0
3. evaluate $\sin(0^\circ)$.
a. $\frac{\sqrt{3}}{2}$ c. 0
b. $\frac{1}{2}$ d. 1
4. using a graphing calculator, examine the graph of $f(x) = -2\sin(x - 4) + 8$. what is the amplitude of the function?
a. 4 c. 8
b. 1 d. 2
5. how often do peaks of a sinusoidal function occur?
a. once each period c. twice each cycle
b. twice each period d. once every 2 cycles

Question

chapter 6 assignment - sinusoidal function
knowledge and understanding /10, communication /10, thinking /10, application /10, total /40
multiple choice knowledge and understanding 10 marks--1 mark each
identify the choice that best completes the statement or answers the question. use only capital letters.
1. what are the peaks of a periodic function?
a. the extremes of the graph  c. the highest points of the graph
b. the lowest points of the graph  d. the x-intercepts of the graph
2. what is the amplitude of the function?
graph of a sinusoidal function with x-axis from -5 to 5 and y-axis from -7 to 7
a. 7  c. 10
b. 14  d. 0
3. evaluate $\sin(0^\circ)$.
a. $\frac{\sqrt{3}}{2}$  c. 0
b. $\frac{1}{2}$  d. 1
4. using a graphing calculator, examine the graph of $f(x) = -2\sin(x - 4) + 8$. what is the amplitude of the function?
a. 4  c. 8
b. 1  d. 2
5. how often do peaks of a sinusoidal function occur?
a. once each period  c. twice each cycle
b. twice each period  d. once every 2 cycles

Accepted Answer

### Question 1
# Brief Explanations:
Peaks of a periodic function are the highest points on its graph. Option A is too vague (extremes include both high and low), B is the lowest points (troughs), D is x - intercepts (where the graph crosses the x - axis, not peaks). So the correct answer is C.
# Answer:
C. the highest points of the graph

### Question 2
# Explanation:
## Step 1: Recall the formula for amplitude of a sinusoidal function $y = A\sin(Bx - C)+D$ or $y = A\cos(Bx - C)+D$. The amplitude is $|A|$, and also, amplitude can be calculated as $\frac{\text{maximum value}-\text{minimum value}}{2}$.
From the graph, the maximum value (peak) is 7 and the minimum value (trough) is - 7.
## Step 2: Calculate the amplitude using the formula $\frac{\text{max}-\text{min}}{2}$.
Substitute max = 7 and min=-7 into the formula: $\frac{7 - (-7)}{2}=\frac{14}{2} = 7$.
# Answer:
A. 7

### Question 3
# Brief Explanations:
We know from the unit - circle definition of the sine function that $\sin(0^{\circ}) = 0$. $\sin(60^{\circ})=\frac{\sqrt{3}}{2}$, $\sin(30^{\circ})=\frac{1}{2}$, and $\sin(90^{\circ}) = 1$. So the correct answer is C.
# Answer:
C. 0

### Question 4
# Explanation:
## Step 1: Recall the general form of a sinusoidal function $y = A\sin(Bx - C)+D$. The amplitude of the function is given by $|A|$.
## Step 2: Identify the value of $A$ in the function $f(x)=- 2\sin(x - 4)+8$.
Here, $A=-2$. The amplitude is $|A|=|-2| = 2$.
# Answer:
D. 2

### Question 5
# Brief Explanations:
A sinusoidal function has a period, and within each period, there is one peak (highest point) and one trough (lowest point). So peaks occur once each period. Option B is incorrect (twice each period would mean two peaks per period, which is not the case for a standard sinusoidal function), C is incorrect (twice each cycle is wrong, as a cycle has one peak), D is incorrect (once every 2 cycles is wrong, a peak occurs once per cycle). So the correct answer is A.
# Answer:
A. once each period

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step 1: Recall the formula for amplitude of a sinusoidal function \(y = A\sin(Bx - C)+D\) or \(y = A\cos(Bx - C)+D\). The amplitude is \(|A|\), and also, amplitude can be calculated as \(\frac{\text{maximum value}-\text{minimum value}}{2}\).

Step 2: Calculate the amplitude using the formula \(\frac{\text{max}-\text{min}}{2}\).

Answer:

Question 2