Linear Trig Equation Word Problem

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The discussion centers on solving a linear trigonometric equation related to a word problem, specifically identifying when the function h(t) is less than zero within a 24-second domain. Participants clarify that no substitution is needed for the 24 seconds, as it defines the time interval for t. Graphing the function is suggested as an effective method to visualize the solution. Additionally, the concept of symmetry in trigonometric functions is mentioned, referring to finding equivalent radian values. Understanding these concepts is crucial for determining the correct intervals where h(t) is negative.
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.
 
Graphing it would be a good start.

"Look for radians that are equivalent in their values." I don't know what that means.
 

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