## cassieforlife5 one year ago Solve the equation in the following intervals: sin x = -0.2 I know for this you have to find sin^-1 (-0.2) and I got -0.201 (my teacher said we have to do it in radians not degrees) but i'm so confused from here! Can anyone explain how to solve it?

1. cassieforlife5

The intervals are: $0 \le x < 2\pi$

2. cassieforlife5

and the second one is: $-\infty < x < \infty$

3. anonymous

$x=-0.201358+2n \Pi$ for $0 \le x < 2\pi$: x=−0.201358+2Π for $-\infty < x < \infty$: x=−0.201358+2nΠ, $n=0,\pm1,\pm2,\pm3,....$

4. cassieforlife5

Thanks for your reply! Can you explain why you add 2pi for the 1st one and 2npi for the second one?

5. anonymous

because the period of sin x is 2Pi, it repeat it self after 2pi.

6. anonymous

for 0≤x<2π : x=−0.201358+2Π this because the interval, −0.201358<0 so this solution is rejected x=−0.201358+2Π is good x=−0.201358+2*2Π>2Π this solution is rejected

7. anonymous

Do you get it?

8. cassieforlife5

oh i see. so i have another question if you can help?

9. cassieforlife5

sec x= -3 for the interval $-\pi \le x < \pi$ 1/cosx=-3 cosx= -1/3 cos^-1 (-1/3)= 1.911 + pi is this the only answer or are there more?

10. cassieforlife5

okay so 1.911-pi is the only answer

11. cassieforlife5

yeah sorry forgot to include that part but i got it

12. cassieforlife5

gosh you're a life saver!! could you check my work for this one as well?

13. anonymous

sorry I made mistake

14. anonymous

x=1.911

15. anonymous

this one solution

16. cassieforlife5

cot x= -1 for -infinity< x < infinity cosx/sinx= -1 3pi/4+ 2pi and 7pi/4+ 2pi ?

17. cassieforlife5

sorry i meant 3pi/4+ npi 7pi/4 + 4pi

18. cassieforlife5

7pi/4+ npi

19. anonymous

for the previous problem the solution is x=1.911

20. cassieforlife5

yeah because you don't subtract possibilities right?

21. anonymous

for the last on :x= 3pi/4+ 2npi and 7pi/4+ 2npi

22. anonymous

*one

23. cassieforlife5

is it 2npi? i thought it was just npi because the period of cotangent is pi?

24. anonymous

cot x=cos x/sin x, so it is contained on two functions, and period of cos x and sin x is 2npi

25. cassieforlife5

oh... alright. sorry for asking so many questions but honestly you made it so much easier!! 2sin(2theta)+$\sqrt{3}$= 0 [0, 2pi) I got 4pi/3 and 5pi/3. It says to give both general and specific solutions, but these were the only ones that fit the intervals

26. anonymous

$2\sin (2\theta)+ \sqrt{3}=0?$

27. cassieforlife5

yeah sorry it got typed awkwardly

28. anonymous

let solve it

29. cassieforlife5

2sin2x= - sqrt(3) sin2x= - sqrt(3)/2 at 4pi/3 and 5pi/3 I've added 2npi, but all the solutions were larger than 2pi so I thought they were invalid

30. anonymous

I got (-pi/6)+npi, (-pi/3)+npi

31. anonymous

this in general without considering the interval

32. cassieforlife5

could you explain? i think it might be because I didn't get rid of the 2 in sin2x= -sqrt(3)/2

33. anonymous

34. cassieforlife5

which one is correct?

35. cassieforlife5

is this right? sin2x= $-\sqrt{3}/2$ 2x= 4pi/3 or 2x= 5pi/3 x= 2pi/3 or 5pi/6

36. anonymous

correct and there are two more solutions.

37. cassieforlife5

2 more? I have no idea how to get them then

38. anonymous

because npi

39. anonymous

and the interval [0, 2pi)

40. cassieforlife5

I thought it was supposed to be 2npi? and i tried that and it went over 2pi

41. anonymous

2x= 4pi/3 +2npi, 5pi/3+2npi x= 2pi/3 +npi, 5pi/6+npi

42. cassieforlife5

Oh I didn't know you added the 2npi before simplifying

43. anonymous

I forget it, you should and it

44. anonymous

for the interval [0, 2pi): $x=\frac{ 2\pi }{ 3 } , \frac{ 2\pi }{ 3 }+\pi=\frac{ 5\pi }{ 3 },\frac{ 5\pi }{ 6 } ,\frac{ 5\pi }{ 6 }+\pi=\frac{ 11\pi }{ 6}$

45. cassieforlife5

yup I checked all 4 answers and they all equalled 0!! 2sin^2x= 2+cosx [0,pi] after using an identity and simplifying, I got cosx(2cosx +1)=0 cosx=0 at pi/2 and 3pi/2 2cosx +1-> cosx= -1/2 at 2pi/3 and 4pi/3 I eliminated 3pi/2 and 4pi/3 because they were bigger than pi so my answers are pi/2 and 2pi/3

46. anonymous

I need to eat my dinner. can we complete it later

47. cassieforlife5

sure! thank you so much for your help!!! i'll work on other things until then

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