Need help with sinusoidal functions

In summary, the book provides information on how to determine precise phase shifting by observing graphs. For the first graph, it is stated that it has horizontally shifted to the right by 15 units. The second graph also shows a shift to the right, but by 80 units. The conversation suggests focusing on the middle of the graph and considering the normal sin function without any left or right shifts. It is also mentioned that the middle value should be at time 0 for zero phase shift.
  • #1
DoomBringer2
4
0
1. Hello everyone, I am having some trouble determining precise phase shifting by observing the graphs.

dRt4B.jpg


book says this graph has horizontally shifted to the right by 15 units. How was this determined? I can't figure it out!

second this graph:
hLXCQ.jpg

Says the graph was shifted 80 units to the right but again how is this determined? Please help thnx
 
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  • #2
Welcome to PF!

Hail DoomBringer2! Welcome to PF! :smile:
DoomBringer2 said:
book says this graph has horizontally shifted to the right by 15 units. How was this determined? I can't figure it out!

Says the graph was shifted 80 units to the right but again how is this determined?

Concentrate on the middle of the graph …

at zero phase shift, it should have that middle value at time 0. :wink:
 
  • #3
Hint: What does the normal sin function look like without any left or right shifts?
 
  • #4
thanks a lot guys and gals, I am about to submit my work. hopefully I got it right lol
 

1. What are sinusoidal functions?

Sinusoidal functions are mathematical functions that follow a sine or cosine curve. They can be used to model periodic phenomena such as sound waves, light waves, and oscillating motion.

2. How do I graph a sinusoidal function?

To graph a sinusoidal function, you will need to identify the amplitude, period, and horizontal shift. Then, plot key points on the curve and connect them to create the sine or cosine curve. Don't forget to label your axes!

3. How do I find the equation of a sinusoidal function?

The general equation for a sinusoidal function is y = A sin(Bx + C) + D or y = A cos(Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. To find the equation, you will need to know at least three key points on the curve.

4. What is the difference between a sine and cosine function?

Sine and cosine functions are very similar, but they differ in their starting point on the x-axis. A sine function starts at (0,0) while a cosine function starts at (1,0). This results in a phase shift of π/2 radians between the two functions.

5. How are sinusoidal functions used in real life?

Sinusoidal functions have many real-life applications, such as modeling the tides, predicting stock prices, and analyzing sound waves. They are also used in engineering and physics to describe periodic motion and analyze oscillating systems.

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