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

[Incog]

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.

 

[chroot]

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

 

[turdferguson]

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.,