# Application Problem

• Feb 28th 2009, 01:37 PM
chrozer
Application Problem
The force $F$ (in pounds) on a person's back when he or she bends over at angle (in degrees) is modeled by

$F = \frac {0.6W\sin {(\Theta + 90)}}{\sin{12}}$

where $W$ is the person's weight (in pounds).

a) Simplify the model.
Would it just be $F = \frac {0.6W\cos {\Theta}}{\sin{12}}$ since $\sin{(\Theta +90)} = \cos{\Theta}$ ?

b) Use a graphing utility to graph the model, where $W = 185$ and $0 < \theta < 90$.
This is done.

c) At what angle is the force a maximum? At what angle is the force a minimum?
The angle is at a maximum at 0 and 360 degrees and minumum at 180 degrees. Does that seem right? Because at 180 degrees $F$ is negative.

I have also attached a picture of the original problem.
• Feb 28th 2009, 01:58 PM
skeeter
look at values of the force for values of $\theta$ between 0 and 90 degrees only.

max F at 0

min F at 90
• Feb 28th 2009, 02:06 PM
chrozer
Quote:

Originally Posted by skeeter
look at values of the force for values of $\theta$ between 0 and 90 degrees only.

max F at 0

min F at 90

Oh yeah. Thanks. Btw, part (a) is right, right?
• Feb 28th 2009, 02:27 PM
skeeter
Quote:

Originally Posted by chrozer
Oh yeah. Thanks. Btw, part (a) is right, right?

graph both the original model and the simplified version ... do the graphs match up?
• Feb 28th 2009, 02:32 PM
chrozer
Quote:

Originally Posted by skeeter
graph both the original model and the simplified version ... do the graphs match up?

They do. That's the simplest it can be simplified right?