## anonymous one year ago Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5

1. Nnesha

set it equal to zero then you will get quadratic equation

2. anonymous

Yeah I noticed that but can you show me how you to set it up

3. Nnesha

$\huge\rm 7\sin^2x-14sinx+2+5=0$ add 5 both

4. Nnesha

to make it easy let sin(x) x $\huge\rm 7x^2 -14x+2+5 =0$ |dw:1437508829146:dw| solve for x :-)

5. anonymous

Ohh okay thanks

6. Nnesha

let me know what you get

7. anonymous

Yeah just give me a min I need to solve another problem real quick

8. Nnesha

sure :=)

9. anonymous

7x^2-14x+7

10. Nnesha

equal to zero 0 then take out common factor

11. anonymous

7(x^2-2x+1)=0

12. Nnesha

opps sorry i didn't get notification

13. Nnesha

and yes that's right now factor this quadratic equation x^2 -2x +1

14. anonymous

7(x-1)(x+1)=0

15. Nnesha

yes right now set these equal to zero $\huge\rm 7 \cancel= 0 ~~~(x-1)=0~~~(x-1)=0$ solve for x

16. anonymous

x=1

17. anonymous

18. Nnesha

yes now change x with sin

19. Nnesha

remember we changed sin(x) with x right ?

20. anonymous

oh yeah

21. Nnesha

so $\huge\rm sinx =1$

22. Nnesha

now use unit circle to find solution

23. anonymous

find where one is 1 is y on the unit circle?

24. Nnesha

(cos , sin) x coordinate represent cos function and y coordinate represent sin function

25. anonymous

would it be pi/2

26. Nnesha

|dw:1437510845962:dw|

27. Nnesha

yep

28. anonymous

thats it, thats the only solution

29. Nnesha

yep right

30. anonymous

oh okay thank you so much!

31. Nnesha

my pleasure but remember sinx = 1 multiplicity of 2

32. anonymous

I'm gonna post another question can you help me with that one as well, I think i know the answer just confused how to get to the answer

33. anonymous

so my answer would be sinx=1^2?

34. Nnesha

no sin x= 1 is right

35. anonymous

oh okay

36. anonymous