Solving the Mod of Sine Equation: What Does Each Number Mean?

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In summary, the equation y = 1.6sin(1.8x - 0.9) + 2.5 represents the vertical position of a person swinging, with the numbers 1.6 and 2.5 representing the vertical stretch and vertical shift, respectively. The value of a represents the distance the person is off the ground, while b and c determine the period and phase shift of the function.
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Incog
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Homework Statement



Guy records data of person using a swing. Comes up with an equation to show his findings: y = 1.6sin(1.8x - 0.9) + 2.5

What does each number represent in relation to the situation (person swinging)?

Homework Equations



Don't think any equations are needed for this. But it's good to know that above equation is derived from y = asin(bx - c) + d

a - vertical stretch/shrink
b - horizontal stretch/shrink
c - horizontal shift
d - vertical shift

The Attempt at a Solution



This one's been killin me. Since the variable 'd' represents the vertical shift, I was guessing the 1.6 may represent the distance the person's off of the ground. And since 'a' is the vertical stretch/shrink, maybe that could represent the maximum height or something. I have no idea what 'b' and 'c' will represent.
 
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  • #2
First, note that the sine wave oscillates between -1 and +1. So, 1.6 sin (...) oscillates between -1.6 and +1.6.

If you take something that oscillates between -1.6 and +1.6, and add 2.5 to it, then it oscillates between -1.6 + 2.5 and 1.6 + 2.5.

- Warren
 
  • #3
There is a relationship between b and the period of the function. Assuming this is a vertical position versus time function, the horizontal shift c is often called a phase shift and tells where equilibrium (y = 0 for a sine function) is in relation to the clock. With no phase shift, the function will be at a maximum at t = pi/2, a minimum at t = 3pi/3, etc.,
 

1. What is the purpose of finding the mod of a sine equation?

The mod of a sine equation helps us understand the periodic nature of the function. It allows us to determine the amplitude, period, and phase shift of the equation, which are important in graphing and solving trigonometric equations.

2. What does the number in front of the sine function represent?

The number in front of the sine function, also known as the amplitude, represents the maximum displacement of the graph from the midline. It determines the height of the peaks and valleys of the graph.

3. How do we determine the period of a mod sine equation?

The period of a mod sine equation is determined by the coefficient of the variable inside the sine function. It can be calculated by dividing 2π by this coefficient.

4. What is the significance of the phase shift in a mod sine equation?

The phase shift in a mod sine equation determines the horizontal translation of the graph. It tells us where the graph starts its cycle, and it can be positive or negative depending on the direction of the shift.

5. How do we solve a mod sine equation?

To solve a mod sine equation, we first need to isolate the sine function and then determine the period and phase shift. From there, we can use our knowledge of the unit circle or trigonometric identities to find the solutions within a given interval. Alternatively, we can use a graphing calculator to visualize the equation and find the solutions.

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