Answer:
![y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2](https://tex.z-dn.net/?f=y%3D4sin%28%5Cfrac%7B2%5Cpi%28t%2B%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%29%20%7D%7B4%5Cpi%20%7D%20%29-2)
Step-by-step explanation:
Let's start with the original function.
![y=a sin\frac{2\pi t}{T}](https://tex.z-dn.net/?f=y%3Da%20sin%5Cfrac%7B2%5Cpi%20t%7D%7BT%7D)
We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4
respectively.
![y=4sin(\frac{2\pi t}{4\pi } )](https://tex.z-dn.net/?f=y%3D4sin%28%5Cfrac%7B2%5Cpi%20t%7D%7B4%5Cpi%20%7D%20%29)
Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:
![y=4sin(\frac{2\pit }{4\pi } )-2](https://tex.z-dn.net/?f=y%3D4sin%28%5Cfrac%7B2%5Cpit%20%7D%7B4%5Cpi%20%7D%20%29-2)
Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:
![y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2](https://tex.z-dn.net/?f=y%3D4sin%28%5Cfrac%7B2%5Cpi%28t%2B%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%29%20%7D%7B4%5Cpi%20%7D%20%29-2)
This function has vertical shift -2, phase shift -4/3
, amplitude 4, and period 4
.
Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.
Answer:
what's the Question???
Step-by-step explanation:
The correct anwer is False
Explanation
According to the graph, it can be seen that a student has four hours of sleep as the minimum number of hours of sleep; two students have six hours of sleep, four students have six and a half hours of sleep, four have seven hours of sleep, three have seven and a half hours of sleep, five have eight hours of sleep, and one has eight and a half hours of sleep as maximum hours of sleep. Therefore, it can be affirmed that the statement that the difference between the maximum amount and the minimum number of hours is two and a half hours is false because between four hours and eight and a half hours there are four and a half hours of difference. So, the correct answer is False.
Answer:
(a) 1, 2, 7, 14 (b) 1, 3, 9, 27 (c) 1, 2, 3, 6 (d) 1, 3, 5, 15 ... 4.4 Sine, Cosine and Tangent. 1. (a) hyp : BC ; adj : AC ; opp : AB. (b) hyp : DF ; adj : DE ; opp : EF. (c).
SO THE ANSWER IS 8
Step-by-step explanation:
Answer:
Notice in my attached drawing that I have located point H in two different locations, point H and point H2 for argument purposes.
Line FE is equal to line GH in length.
angle at corner F is 95 degrees.
The angle at point E varies with the location of point H, or with the length of line FG.
More information is needed to determine an exact angle at point E.