Please help i dont know how to do this. Can someone give the answers and how its done?

Question

Please help i dont know how to do this. Can someone give the answers and how its done?

The force F (in pounds) on a person's back when he or she bends

over at an angle e from an upright position is modeled by

F= 0.6W sin (θ+90)/ sin 12°

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

(a) Simplify the model.

(b) Use a graphing utility to graph the model, where

W = 185 and 0° < θ< 90°. (Link if you can plz)

(c) At what angle is the force maximized? At what angle is the force

minimized?

Answer 1

sin (θ+90) = sin θ cos 90 + cos θ sin 90 = 0 + cos θ = cos θ

so simplified F = 0.6W cos θ / sin 12

you could evaluate 0.6 / sin 12 = 2.8858 .... but this will not be exact so I would not do so.

You can just graph it on Desmos. Make sure Desmos is set to degrees. y = 0.6 x 185 x cos (x) / sin (12)

set the scale on the x axis from 0-90

Then for the last part, you are looking for the highest and lowest values of y on your graph. Then read off the corresponding value of x.

Or you can think about cos(x). 0 <=x < 90, cos (x) is maximum when x =0, and minimum when x=90.

So F will be maximum when x=0 [standing straight up] and minimum when x=90 [bending over at 90]