## joachimngeny one year ago 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

1. joachimngeny

im stuck with the second solution

am i wrong

3. joachimngeny

@madhu.mukherjee.946 i just realised i didnt attach the equation sin(7 x) = 0.64

ok now its f9

5. joachimngeny

@Michele_Laino i just realise that i have to give answer in radian

6. Michele_Laino

hint: |dw:1440747531526:dw|

did you get the value of x

8. Michele_Laino

the smallest solution (in radians) is: $\Large {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992$

9. joachimngeny

i got x1 = 0.10 and X2= 3.04

10. Michele_Laino

whereas the second one, is: $\Large {x_2} = \pi - 0.0992 = ...?$

11. Michele_Laino

I have used windows calculator and the "radians" option

12. Michele_Laino

13. Michele_Laino

since you have used approximated values

14. joachimngeny

@Michele_Laino apparently my answer is partially wrong.

15. joachimngeny

I must have rounded it off wrong or something

16. Michele_Laino

yes! you have rounded off the smallest solution, nevertheless it is not a wrong answer

17. joachimngeny

@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

18. Michele_Laino

here is the right setting on windows calculator

19. joachimngeny

@Michele_Laino is that what you got for the smallest value?

20. joachimngeny

im on mac computer atm

21. Michele_Laino

no, it is the smallest value multiplied by 7, namely: 7*x1=0.6944

22. Michele_Laino

as you can see from my image, there is the formula: "asinr(0.64)" at the upper right corner

23. Michele_Laino

now, in order to get the value of x1, you have to divide 0.694498... by 7, so you get this: 0.0992...

24. joachimngeny

yes i understand. this is what i answered

25. joachimngeny

@Michele_Laino

26. Michele_Laino

27. joachimngeny

what i did seem right, yeah?

28. Michele_Laino

29. Michele_Laino

ok! I'm here

30. joachimngeny

@Michele_Laino did you see my previous reply

31. Michele_Laino

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: $\Large 7{x_1},7{x_2}$

32. Michele_Laino

therefore: $\Large \begin{gathered} {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992, \hfill \\ \hfill \\ {x_2} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} \hfill \\ \end{gathered}$

33. Michele_Laino

number of solution is correct, namely, we have 14 solutions

34. Michele_Laino

and the highest solution is: $\Large {x_2} + 6 \cdot \frac{{2\pi }}{7}$

35. joachimngeny

I don't know why it says partially wrong.

36. joachimngeny

@Michele_Laino but isnt that outside the range? 0 -> 2pi?

37. Michele_Laino

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: $\Large {x_2} + 6 \cdot \frac{{2\pi }}{7} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} + 6 \cdot \frac{{2\pi }}{7} = 5.735$

38. Michele_Laino

namely 3.04 is wrong, please replace it with 5.735

39. Michele_Laino

better is 5.74

40. joachimngeny

@Michele_Laino ok thank you. I appriciate your help

41. Michele_Laino

:)