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
AVprozaik [17]
2 years ago
14

Write a sine and cosine function that models the data in the table. I need steps to both the sine and cosine functions for a, b,

c, and d. I need a good explantion. Thank you!

Mathematics
1 answer:
dangina [55]2 years ago
4 0

Answer(s):

\displaystyle y = -29sin\:(\frac{\pi}{6}x + \frac{\pi}{2}) + 44\frac{1}{2} \\ y = -29cos\:\frac{\pi}{6}x + 44\frac{1}{2}

Step-by-step explanation:

\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 44\frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-3} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{6}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{12} \hookrightarrow \frac{2}{\frac{\pi}{6}}\pi \\ Amplitude \hookrightarrow 29

<em>OR</em>

\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 44\frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{12} \hookrightarrow \frac{2}{\frac{\pi}{6}}\pi \\ Amplitude \hookrightarrow 29

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of <em>sine</em>, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of \displaystyle y = -29sin\:\frac{\pi}{6}x + 44\frac{1}{2},in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the <em>cosine</em> graph [photograph on the left], accourding to the <u>horisontal shift formula</u> above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY <em>REALLY</em> ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the <em>sine</em> graph [centre photograph] is shifted \displaystyle 3\:unitsto the right, which means that in order to match the <em>co</em><em>sine</em> graph [photograph on the left], we need to shift the graph BACKWARD \displaystyle 3\:units,which means the C-term will be negative, and by perfourming your calculations, you will arrive at \displaystyle \boxed{3} = \frac{-\frac{\pi}{2}}{\frac{\pi}{6}}.So, the sine graph of the cosine graph, accourding to the horisontal shift, is \displaystyle y = -29sin\:(\frac{\pi}{6}x + \frac{\pi}{2}) + 44\frac{1}{2}.Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \displaystyle [12, 15\frac{1}{2}],from there to the y-intercept of \displaystyle [0, 15\frac{1}{2}],they are obviously \displaystyle 12\:unitsapart, telling you that the period of the graph is \displaystyle 12.Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the <em>midline</em>. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \displaystyle y = 44\frac{1}{2},in which each crest is extended <em>twenty-nine </em><em>units</em> beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the cosine graph in the photograph farthest to the right is the OPPOCITE of the cosine graph in the photograph farthest to the left, and the reason for this is because of the <em>negative</em> inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of <em>any</em> trigonometric equation, the whole graph reflects over the<em> midline</em>. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

You might be interested in
In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre
babunello [35]

Answer:

About 786 would be expected to yield more than 180 bushels of corn per acre

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the zscore of a measure X is given by:

6 0
3 years ago
Evaluate : limx→ tan2-sin2x x3
GrogVix [38]

Given:

\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}

Solve:

\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}

Use l'hopital's rule:

\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}

Simplify:

\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}

Apply the constant multiple rule:

\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}

Similary :

\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}

8 0
1 year ago
You deposit $200 each month into an account earning 3% interest compounded monthly.
pochemuha

Answer:

here you can do it and other problems you have https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator

Step-by-step explanation:

6 0
3 years ago
Find the real numbers x and y that make the equation true (x+6i)=(3-i)+(4-2yi)​
Ronch [10]

Answer:

x = 7

y = -7/2

Step-by-step explanation:

(x+6i)=(3-i)+(4-2yi)​

First look at the real parts

x = 3 +4

x = 7

Then look at the imaginary part

6i= -i -2yi

6 = -1-2y

Add 1 to each side

6+1 = -2y

7 = -2y

Divide by -2

7/-2 = y

5 0
3 years ago
Find the range of f(x)=-2x + 6 for the domain {-1, 3, 7, 9}
Blizzard [7]

Answer:

range {4, 12, 20, 24}

Step-by-step explanation:

Plug each of the numbers in for x and solve for y

3 0
3 years ago
Other questions:
  • How do you write a ratio for NINE SLICES OF PIZZA FOR SEVEN KIDS?
    14·1 answer
  • What is 3(2x-4)=5x+2
    6·1 answer
  • Geometry Question? Please Help
    10·1 answer
  • PLEASE HURRY AND HELP A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
    11·1 answer
  • Please help!!!! It’s #14 and explain and show me how to do it please
    8·1 answer
  • How many regular hexagons meet at a vertex to form a regular tessellation? 2 3 4 6
    8·2 answers
  • A recipe requires 3 cups of flour to make 27 dinner rolls. How much flour is needed to make 9 rolls?Mandy runs 4 km in 18 min. S
    8·1 answer
  • 4) WILL MAKE BRAINLIEST <br><br> write the slope-interception form of the equation of each line.
    10·1 answer
  • The temperature at noon is 75 degrees. The temperature drops 3 ½ degrees every half hour because a cold front starts coming thro
    8·1 answer
  • Karita had $138.72 in her checking account. She wrote check to take out $45.23 and $18.00, and then made a deposit of $75.85 int
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!