Question in Derivative and limits substitution

I am going through the solution of a problem and i dont understand how he got the values for theita ( see attachment)

0<theita<1.3694

obviously after the transformation of X as a function of cos Theita , there is some limit transformation as well.

Any input would be appreciate it.
4-6.doc
c_hocklandAsked:
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TommySzalapskiConnect With a Mentor Commented:
x = (1-cos(theta))*c/2
So x/c = (1-cos(theta))/2

For 0 <= x/c <= .4 then translates to
For 0 <= (1-cos(theta))/2 <= .4

Solve that for theta and you will see that theta is bounded by 0 and 1.3694
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ozoCommented:
It might help to know what problem was being solved, but it would seem to be because -0.05 + .25*cos(theta) > 0
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c_hocklandAuthor Commented:
let me post the question and complete solution Ozo
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c_hocklandAuthor Commented:
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