hannahg 2 years ago Find all solutions in the interval [0, 2π). sin2x + sin x = 0

1. .Sam.

Do you know what's the identity for sin2x?

2. hannahg

noo i forgot..

3. .Sam.

sin2x=2sinxcosx

4. .Sam.

So how do you proceed?

5. hannahg

2sinx+cosx+sinx=0 right? what do i do next?

6. .Sam.

no, it should be from sin2x + sin x = 0 to 2sinxcosx + sin x =0 right?

7. hannahg

ohh yea

8. .Sam.

you should try factoring now

9. hannahg

sinx(2cosx+1)=0 is this right? what do i do next? o.O

10. AravindG

ya u r right :)

11. .Sam.

yes, now you can let sinx=0 and 2cosx+1=0 then find the x values

12. AravindG

equate that to 0 and find x values

13. hannahg

so i got cosx=-1/2 how do i find the value of x?

14. .Sam.

well you can do this cosx=-1/2 x=cos^{-1} (-1/2)

15. hannahg

so what are all possible values of x? 0 and......what else O.o

16. AravindG

17. .Sam.

no its not 0

18. hannahg

@AravindG :)

19. .Sam.

you calculate cos^(-1) 1/2 first without minus on half you'll get 60 degrees

20. hannahg

yes:)

21. .Sam.

then use this chart for cosine |dw:1358873950517:dw| we are looking at the minus side since we got minus half. then 180-60=120 degrees 180+60=240 degrees

22. AravindG

@hannahg thats better :)

23. hannahg

yes. so all the possible solutions will be pi, pi/3, 2pi/3?

24. .Sam.

you still have sinx=0 to do

25. hannahg

yes......! so 0?

26. .Sam.

yes but dont forget about 180

27. .Sam.

|dw:1358874634831:dw|

28. .Sam.

since theta is 0, then you get 180

29. hannahg

@.Sam. so what are all solutions in the interval??