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

1. amoodarya

hint : write sin(2x)=2sinx cos x it will be easy to solve

2. anonymous

Thanks (: But, how do you find solutions? I'm not sure where to begin.

3. anonymous

@amoodarya I wrote out the equation, but am stuck where to begin.

4. amoodarya

let's do it step by step

5. anonymous

Ok (:

6. amoodarya

a question ? is it sin(2x) or sin^2(x)

7. anonymous

The equation is: 7sin^2(x)-14sinx+2=-5

8. amoodarya

$7\sin^2(x)-14sinx+2=-5\\7\sin^2 x-14 sinx +2+5=0\\7\sin^2 x-14 sinx +7=0\\ \div 7\\sin^2x-2sinx+1=0\\(sinx-1)^2=0\\$

9. anonymous

So, to find the solutions, I just solve for x in the equation: (sinx-1)^2=0?

10. amoodarya

yes . can you go on ?

11. anonymous

Yes, I've got it now, thanks!! (:

12. anonymous

Wait...actually. Could you explain how to find the solutions? I'm still unsure what to do about finding the solutions.

13. anonymous

@amoodarya ^^ (:

14. amoodarya

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15. anonymous

So, would my answers be pi/2 and 3pi/2?

16. anonymous

^ @amoodarya