Linear Trig Equation Word Problem

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aeromat
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Homework Statement


pg426-427-12.png

Homework Equations


doubleangleformulae.png

cmpdangleformulae.png


The Attempt at a Solution


The part I don't understand is what would be substituted (if anything) for the 24s? How will that be implemented to solve for the periods of time?
 
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You aren't supposed to substitute anything for the 24 seconds. That is the domain for t in this problem. The problem is asking, for what values of t in [0, 24], is h(t) < 0.
 
Ok so you would just graph it and use symmetry analysis to pick out the intervals right? Symmetry meaning look for radians that are equivalent in their values.