## anonymous one year ago Solve the following equation for theta where 0 < or= theta < 2 pie sin ^2 theta = sin theta

1. freckles

$\sin^2(\theta)-\sin(\theta)=0$ factor left hand side

2. anonymous

is that (sin theta) (sin theta)???

3. freckles

yes x^2 can be written as x*x

4. anonymous

so... now what?

5. freckles

factor

6. freckles

$x^2-x \\ x(x-1)$ you try factoring $\sin^2(\theta)-\sin(\theta)$ it is the same way as I did the expression of x

7. freckles

$x^2=x \\ x^2-x=0 \\ x(x-1)=0 \\ \text{ set both factors equal to zero } \\ x=0 \text{ or } x-1=0 \\ x=0 \text{ or } x=1$

8. freckles

you try solving for sin(theta) now it is the same way

9. freckles

once you have solved for sin(theta) then you will easily be able to find theta

10. anonymous

hold on, don't leave yet

11. anonymous

sin =0 sin theta = 0

12. anonymous

I have no idea what to do next

13. freckles

well you have one equation correct but you are missing an equation

14. freckles

have you not factored $\sin^2(\theta)-\sin(\theta)$ yet?

15. freckles

do you see both sin^2(theta) and sin(theta) have a common factor?

16. freckles

as you said sin^2(theta) can be written as sin(theta)*sin(theta) therefore sin(theta) and sin^2(theta) both have the common factor sin(theta)

17. freckles

so you can factor that out of the expression

18. freckles

$\sin^2(\theta)-\sin(\theta)=0 \\ \sin(\theta)(\sin(\theta)-1)=0$ that is what you should get for the left hand side after factoring now set both factors equal to 0

19. freckles

you can use the unit circle to solve both equations

20. anonymous

wait hold on

21. anonymous

where did you get these 2 equations?

22. freckles

which two?

23. anonymous

wait nvm

24. anonymous

ok but how do you use the unit circle for this? i'm lost

25. freckles

do you know which equations you are solving?

26. anonymous

sin^2 theta - sin theta = 0

27. freckles

you need to factor the left hand side

28. freckles

I have actually done this for you

29. anonymous

I know x factor, but don't know how

30. freckles

|dw:1433565703539:dw|

31. freckles

now set both factors equal to 0

32. freckles

you have sin(theta)=0 or sin(theta)-1=0

33. freckles

find when sin(theta) is 0 on the unit circle find when sin(theta) is 1 on the unit circle

34. freckles

in other words you are looking for where the y-coordinate is 0 on the unit circle and also looking for when the y coordinate is 1 on the unit circle

35. anonymous

the answer is pie/2 and pie

36. anonymous

but how is it pie though???

37. anonymous

nvm

38. anonymous

got it

39. freckles

so you don't get that sin(pi)=0? also sin(0)=0 so I think you mean you have 0,pi/2,pi

40. anonymous

ok thx