1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olchik [2.2K]
3 years ago
15

A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a

reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Mathematics
1 answer:
mezya [45]3 years ago
4 0

Answer:

  • See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

     y=sin(x)

That function has:

  • Midline, also known as rest or equilibrium position: y = 0
  • Minimum: - 1
  • Maximum: 1
  • Amplitude: the distance between a minimum or a maximum and the midline = 1
  • period: the interval of repetition of the function = 2π

The more general sine function is:

             y=Asin(Bx+C)+D

That function has:

  • Midline: y = D (it is a vertical shift from the parent function)
  • Minimum: - A + D
  • Maximum: A + D
  • Amplitude: A
  • period: 2π/B
  • phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

  • Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
  • Amplitude, A = 3
  • midline y = - 1 ⇒ D = - 1
  • y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

       

            y=3sin(2x/\pi+C)-1

Substitute (0, -1)

             

              -1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0

Hence, the function to graph is:

              y=3sin(\pi x/2)-1

To draw that function use this:

  • Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
  • Minima: 3(-1) - 1 = - 3 - 1 = -4
  • y-intercept: (0, - 1)
  • x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
  • first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

You might be interested in
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such tha
natita [175]

Answer:

Step-by-step explanation:

Given that:

Population Mean = 7.1

sample size = 24

Sample mean = 7.3

Standard deviation = 1.0

Level of significance = 0.025

The null hypothesis:

H_o: \mu = 7.1

The alternative hypothesis:

H_a: \mu > 7.1

This test is right-tailed.

degree \ of \  freedom=  n - 1 \\ \\ degree \  of \  freedom  =  24 - 1 \\ \\ degree \ of \  freedom   = 23

Rejection region: at ∝ = 0.025 and df of 23, the critical value of the right-tailed test t_c = 2.069

The test statistics can be computed as:

t = \dfrac{ \hat X - \mu_o}{\dfrac{s}{\sqrt{n}}}

t = \dfrac{ 7.3-7.1}{\dfrac{1}{\sqrt{24}}}

t = \dfrac{0.2}{0.204}

t = 0.980

Decision rule:

Since the calculated value of t is lesser than, i.e t = 0.980 < t_c = 2.069, then we do not reject the null hypothesis.

Conclusion:

We conclude that there is insufficient evidence to claim that the population mean is greater than 7.1 at 0.025 level of significance.

6 0
3 years ago
What is the constant of variation, k, for the table?
allochka39001 [22]
K = -2/3

Explanation:

7 0
3 years ago
Use the set B = {5, 7, 9, 11} to determine n(B).<br> n(B) = 0
kkurt [141]

9514 1404 393

Answer:

  n(B) = 4

Step-by-step explanation:

There are four (4) elements in set B.

  n(B) = 4

5 0
3 years ago
The acceleration of car that comes from a velocity of 10m/s in distance of 25m is​
eimsori [14]

Answer:

what is the time given ???

Step-by-step explanation:

either initial velocity is 0 or final velocity is zero

V=U+AT

converting it we get

V/T = u+a

V/T - U= a

where

v= final velocity

u= initial velocity

a= acceleration

t= time

plz write the full question

8 0
3 years ago
Find the area in the shaded region.
irinina [24]
The answer should be 227 ft
7 0
2 years ago
Read 2 more answers
Other questions:
  • What is the answer to 3a+5-x+7x-2a
    15·1 answer
  • Select the letter of the best answer choice. Use 3.14 or 22/7 for π
    9·1 answer
  • I confused a lot plz help
    8·2 answers
  • What is the equation of a line through the points (0, 9) and (3, 0)?
    12·2 answers
  • Two factors are multiplied and their product is 34.44 one factor is a whole number what is the least number of decimal places in
    10·1 answer
  • Translate the phrase into an algebraic three dollars more than twice the cost of a bowl of soups 2+3
    11·1 answer
  • Tan C= <br> Help help help
    9·2 answers
  • If Angelica is 5 steps to the right of the classroom door and Brion is 12 steps to the left
    9·1 answer
  • Please help will mark brainlist answer ! <br><br> Find the length of AB<br><br> AB =
    11·1 answer
  • 30 points help me ASAP
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!