1. ## 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.

2. look at values of the force for values of $\theta$ between 0 and 90 degrees only.

max F at 0

min F at 90

3. 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?

4. 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?

5. 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?