## HelpMe94 3 years ago Sin(2x)*Sin(x)=Cos(x) ..... Solve X

1. HelpMe94

Sin(2x)= 2Sin(x)Cos(x)

2. HelpMe94

So I Got ..... (2Sin(x)Cos(x)Sin(x))-Cos(x)=0

3. HelpMe94

Now What?

4. mark_o.

try factoring them (2Sin(x)Cos(x)Sin(x))-Cos(x)=0

5. HelpMe94

How?

6. HelpMe94

@mark_o. How?

7. HelpMe94

Cos(x) (2 Sin(x) Sin(x))-1=0

8. HelpMe94

Cos(x) (2Sin(x)Sin(x))=1

9. mark_o.

hm lets try this (2Sin(x)Cos(x)Sin(x)) = Cos(x) divide both sides by cos x then (2Sin(x)Sin(x)) = 1 can you continue from here?

10. HelpMe94

@mark_o. is it possible to combine the sines?

11. mark_o.

yes

12. HelpMe94

How?

13. mark_o.

(2Sin(x)Sin(x)) = 1 multiplying 2[Sin(x)]^2 = 1

14. HelpMe94

oh i didn't see that 2 was not part of sine

15. mark_o.

ok from here 2[Sin(x)]^2 = 1 [Sin(x)]^2 = 1/2

16. HelpMe94

ok then Sin(x)^2 = 1-Cos(2x)/2 Right?

17. mark_o.

nope, use power of i/2 on both sides from [Sin(x)]^2 = 1/2 ([Sin(x)]^2)^1/2 = sqrt(1/2) correct? yes or no?

18. HelpMe94

How would this make it solve so i get answers to the unit circle?

19. mark_o.

([Sin(x)]^2)^1/2 = sqrt(1/2) $\sin x=\sqrt{\frac{ 1 }{ 2 }}=\frac{ 1 }{ \sqrt{2} }*\frac{ \sqrt{2} }{ \sqrt{2} }=...?$

20. HelpMe94

X=pi/4

21. mark_o.

yes...you are correct x=45deg =pi/4

22. HelpMe94

although this seems not right there should be more to this.... because i thought.... Sin(2x)Sin(x)=Cos(x) Sin(2x)Sin(x)-Cos(x)=0 2Sin(x)Cos(x)Sin(x)-Cos(x)=0 Cos(x)(2Sin(x)Sin(x))=1 Then Maybe..... Cos(x)(2Sin(x)Sin(x))=1 Cos(x)=1 and 2Sin(x)=1 and Sin(x)=1

23. HelpMe94

Attached is a example of this..

24. HelpMe94

if it is then Cos(x)=1 has solutions 0 and 2pi 2Sin(x)=1 also as Sin(x)=1/2 solutions pi/6 and 5pi/6 Sin(x)=1 solution pi/2

25. mark_o.

yesssssss thats right 2Sin(x)Cos(x)Sin(x)-Cos(x)=0 could be like Cos(x)[(2Sin(x)Sin(x))-1]=0 cos x=0 and 2Sin(x)Sin(x))-1=0 x= arc cos 0 x=90deg=pi/2 and for 2Sin(x)Sin(x))-1]=0 2Sin(x)Sin(x))=1

26. HelpMe94

as long as restrictions are [0,2pi)

27. mark_o.

yes you got it.. lol..:D

28. HelpMe94

oh that makes so much more sense after the factoring and combining of sines... lol