This graph looks like a trigonometric function. Which trigonometric function would be best to use for this model: cosine, sine, or tangent? Why?

Type your response here:


a. It’s time to start making your model fit the path of the mass. Start with amplitude. What is the amplitude of the weight’s motion? How can you modify the base trigonometric function you identified in part b to fit this amplitude? Do this now.

Type your response here:


b. What is the period of the weight’s motion? How can you modify the trigonometric function you identified in part c to fit this period? Do this now.

Type your response here:



c. Check how your model looks compared with the mass by graphing your model with the Edmentum Graphing Tool. Looking at the graph, what is different between your model and the graph of the mass? What needs to change to make your model more accurate? Make this change to your model, and type in the new equation for your model.

Type your response here:

[tex]\displaystyle \boxed{y = \frac{6}{25}cos\:(1\frac{1}{2}\pi{x} - \frac{\pi}{2})} \\ \\ 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 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{3}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{1}{2}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}} \hookrightarrow \frac{2}{1\frac{1}{2}\pi}\pi \\ Amplitude \hookrightarrow \frac{6}{25}[/tex]

OR

[tex]\displaystyle \boxed{y = \frac{6}{25}sin\:1\frac{1}{2}\pi{x}} \\ \\ 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 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}} \hookrightarrow \frac{2}{1\frac{1}{2}\pi}\pi \\ Amplitude \hookrightarrow \frac{6}{25}[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = \frac{6}{25}cos\:1\frac{1}{2}\pi{x},[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is approximately shifted [tex]\displaystyle \frac{1}{3}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{3}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{1}{3}} = \frac{\frac{\pi}{2}}{1\frac{1}{2}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = \frac{6}{25}cos\:(1\frac{1}{2}\pi{x} - \frac{\pi}{2}).[/tex]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 hits [tex]\displaystyle [-2\frac{2}{3}, 0],[/tex]from there to [tex]\displaystyle [-1\frac{1}{3}, 0],[/tex]they are obviously [tex]\displaystyle 1\frac{1}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 1\frac{1}{3}.[/tex]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 midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended six-twenty-fifths unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**Now, it really does not matter which function you use because the result will always be the same, but IF the system only wants one function as an answer, then it would be the sine function sinse it intersects the origin. Other than that, it does not matter which one is chosen.

I am delighted to assist you at any time.

If you triple 4 and subtract 2 each day, how many days until you have zero?* 2 6 8 12

Help!! Image attached, will put most brainliest

How many different nine player batting orders can be chosen from a baseball team of 16?

explain how complex fractions can be used to solve problems involving ratios

Vincent is giving cakes to some children at a carnival. He has 2 strawberry cakes, 6 pineapple cakes, and 7 chocolate cakes. If Vincent selects a cake randomly without looking, what is the probability that he will give a pineapple cake to the first child and then a strawberry cake to the second child? (5 points)


6 over 15 multiplied by 2 over 14 is equal to 12 over 210

6 over 15 plus 2 over 14 is equal to 114 over 210

6 over 15 multiplied by 2 over 15 is equal to 12 over 225

6 over 15 plus 2 over 15 is equal to 8 over 15

What is 25 degrees lower than 57

explain the place value relationship when the same two digits are next to each other in a multidigit number

Solve the equation for 10 points

6x+7=8x−15

Write this number in word form

Number:284028

it is a fraction. it is greater than 0.5 and less than 0.9. its denominator is a square number.its numerator number is a prime number. what could be the mystery number be?

The following table shows the monthly charges for subscribing to the local newspaper.

Number of Months
1
2
3
4
5
Total Cost ($)
15.25
30.50
45.75
61.00
76.25

Identify the independent and dependent variables in the newspaper subscription table.
a.
independent -- Total Cost
dependent -- Number of Months
c.
independent -- Total Cost
dependent -- Month of the Year
b.
independent -- Cost per Paper
dependent -- Number of Months
d.
independent -- Number of Months
dependent -- Total Cost

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?
3
18
21
215

which of the following best describes a regular polygon when the sum of its interior angles is 1080 degrees A.) octagon B.) heptagon C.) hexagon D.) nonagon

An amusement park sells child and adult tickets at a ratio of 8 to 1. On Saturday they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday?

how long would it take for an egg dropped from a helicopter to fall 256 feet to the ground? d=16t^2

You need to pump water out of a flooded basement, using two 50-gallon-per-minute (gpm) pumps. The basement has the dimensions shown and is flooded to a depth of 16 inches. How long will it take to pump the water out of the basement?

Mr. Wilson has 3000 in his bacon count Mrs. Nelson has 10 times as much money in her bank account as Mr. Wilson has in his big and count how much money does Mrs. Nelson have in her bank account

A box has dimensions of 19 inches long, 1.7 feet wide, and 6 inches high. What is the volume of the box? The formula for the volume is V = l ⋅ w ⋅ h.

193.8 cubic inches (in3)
2325.6 cubic inches (in3)
1.35 cubic inches (in3)
16.15 cubic inches (in3)

According to the fundamental theorem of algebra, how many zeros does the function f(x) = 4x3 − x2 − 2x + 1 have?

If trap is an isosceles trapezoid, what is the value of x

Find the outlier of the set of data: 24, 37, 33, 31, 28, 25, 33, 12

what is the value of x and y

Rita bought fabric and ribbon from a store the ribbon cost $18.50 rita paid the cashier $50.00 and received change of $5.25 how much did the fabric cost

HHHHHHEEEELLLLLLPPPPP
Line A: 2x + 2y = 8 Line B: x + y = 4 Which statement is true about the solution to the set of equations? It is (8, 4). It is (4, 8). There is no solution. There are infinitely many solutions.

A caters fee is based on the number of meals she provides. How much is the price per meal if the total fee is $1,088 for 64 meals?

If the area of a rectangle is 24a2b and the length is 8ab2, what would be the width of the rectangle, given that width is found by dividing area by length? Simplify the answer.

the quantity of 3 times a all over b
b over the quantity 3 times a
3 over the quantity a times b
3ab

6x + 2y = 12 solve for y

91 more than the square of a number in verbal form

In a rain forest, it typically rains 290 days out of the year. If it rains today, what is the probability that it will rain tomorrow?

a. 72%
b. 81%
c. 79%
d. 61%

Jack wants to fill a rectangular box with sand. The length of the sand box is 3 feet, width is 6 inches, and height is 2.4 inches. Each bag of sand contains 0.15 cubic foot of sand. How many bags of sand will Jack need to fill the box completely? [1 foot = 12 inches] numerical answers expected