Question 1045052
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sin(7x)=0.43 find the smallest , largest and number of solutions.
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<pre>
The formulation is not accurate.
The accurate formulation is as follows:


    sin(7x)=0.43. Find the smallest solution, the largest solution and the number of solutions in the interval [{{{0}}},{{{2pi}}}).


OK. Sine has 7 full periods in this interval, and in each period the equation has exactly two solutions,
so the total number of solutions is 2*7 = 14.

To find the smallest, write  7x = arcsin(0.43) = 0.4444 (aproximately). (Here I used my calculator. You can use yours)

Hence, x = {{{(1/7)*0.4444}}} = 0.0635 (approx.). It is the smallest solution.

The next solution after that is  7x = {{{pi-arcsin(0.43)}}},

and the largest is  {{{7x[largest]}}} = {{{(pi-arcsin(0.43)) + 6*2pi)}}},  or

{{{x[largest]}}} = {{{(1/7)*(pi-arcsin(0.43) + 6*2pi)}}}.

You can calculate it on your own using this formula.
</pre><TABLE> 
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{{{graph( 330, 330, -1.5, 6.5, -1.5, 1.5,
          sin(7x), 0.43
)}}}


Plots y = {{{sin(7x)}}} and y = 0.43

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