can someone help with this. find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π

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can someone help with this. find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π

Mathematics
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im stuck with the second solution
am i wrong
@madhu.mukherjee.946 i just realised i didnt attach the equation sin(7 x) = 0.64

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ok now its f9
@Michele_Laino i just realise that i have to give answer in radian
hint: |dw:1440747531526:dw|
did you get the value of x
the smallest solution (in radians) is: \[\Large {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992\]
i got x1 = 0.10 and X2= 3.04
whereas the second one, is: \[\Large {x_2} = \pi - 0.0992 = ...?\]
I have used windows calculator and the "radians" option
your answer is correct!
since you have used approximated values
@Michele_Laino apparently my answer is partially wrong.
I must have rounded it off wrong or something
yes! you have rounded off the smallest solution, nevertheless it is not a wrong answer
@Michele_Laino could you show me how to get it right, using radian? Becuase i found the angles in degree then i changed it to radians that probably why im losing marks
here is the right setting on windows calculator
@Michele_Laino is that what you got for the smallest value?
im on mac computer atm
no, it is the smallest value multiplied by 7, namely: 7*x1=0.6944
as you can see from my image, there is the formula: "asinr(0.64)" at the upper right corner
now, in order to get the value of x1, you have to divide 0.694498... by 7, so you get this: 0.0992...
yes i understand. this is what i answered
I'm reading...
what i did seem right, yeah?
please wait a moment, I have to answer to my phone...
ok! I'm here
@Michele_Laino did you see my previous reply
yes! I see, I'm sorry the second solution is: \[\Large 7{x_2} = \pi - 7{x_1} = \pi - \left( {7 \cdot 0.0992} \right) = ...?\] because, from my drawing above I get these values: \[\Large 7{x_1},7{x_2}\]
therefore: \[\Large \begin{gathered} {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992, \hfill \\ \hfill \\ {x_2} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} \hfill \\ \end{gathered} \]
number of solution is correct, namely, we have 14 solutions
and the highest solution is: \[\Large {x_2} + 6 \cdot \frac{{2\pi }}{7}\]
I don't know why it says partially wrong.
@Michele_Laino but isnt that outside the range? 0 -> 2pi?
I think that tne first value, namely 0.1 is right, the third value, namely 14 is also right, you have to correct the second value, namely: \[\Large {x_2} + 6 \cdot \frac{{2\pi }}{7} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} + 6 \cdot \frac{{2\pi }}{7} = 5.735\]
namely 3.04 is wrong, please replace it with 5.735
better is 5.74
@Michele_Laino ok thank you. I appriciate your help
:)

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