Please help to provide the working sol and explanation to get the range of [a,b]. Appreciate the guidance .

[jamestan]

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[Harry_the_cat]

I suggest you consider the graph of the function.

 

[Dr.Peterson]

View attachment 29036t

I would start by observing that both terms involve sin(x), which varies between -1 and 1. If we replace sin(x) with u, we have u + |6u|; think about how to get the largest and smallest values of this. Or write it as a piecewise function.