nikakuz 2 years ago Name five x values for which the sine function equals to 0. Please help!!

1. Mertsj

Are you familiar with the unit circle?

2. nikakuz

no

3. Mertsj

Then find the inverse sine of 0 and and 360 to that answer repeatedly until you have 5 values.

4. nikakuz

how?

5. Mertsj

6. nikakuz

I don't know how though

7. Mertsj

inverse sin 0 enter

8. Mertsj

What in the world are you doing that you don't know anything about the unit circle and don't know how to use your calculator?

9. nikakuz

i put sin 0 enter and the answer was 0 how do i get 5 values?

10. nikakuz

trying to learn from an oonline classs

11. Mertsj

|dw:1375670932781:dw|

12. Mertsj

Have you ever seen that before?

13. nikakuz

yeah

14. Mertsj

That is the unit circle. It is called the unit circle because the radius is 1 unit. The sin is like y.

15. Mertsj

Do you see that the y value is 0 at 0 degrees and 180 degrees?

16. nikakuz

yes

17. Mertsj

Your problem says to give 5 values for which the sin is 0. There are two of them right there: 0 degrees and 180 degrees. If we would go around the circle another time, we would come to 360 degrees and 180+360 which is 540 degrees. Are you with me?

18. nikakuz

sorta.. so it would be 0,180,540?

19. Mertsj

0,180,360,540... Just keep adding 180 degrees because every 180 degrees, the y value (which is the sin) is 0.

20. Mertsj

Or, instead of rotating counterclockwise, we could go clockwise and then the angles would be -180, -360, -540, ...

21. nikakuz

ohh ok thank you! i have the same question exept its cosine value

22. Mertsj

Same thing except the cosine is like x.

23. Mertsj

So where is the cosine 0 on the unit circle?

24. nikakuz

um im not sure

25. Mertsj

Look at the picture I drew. For what angles is the x value 0?

26. Mertsj

|dw:1375671563924:dw|

27. Mertsj

How many degrees is that?

28. nikakuz

90?

29. Mertsj

Yes.

30. Mertsj

And what is the next angle where the x value is 0?

31. nikakuz

so it would be 90 180...?

32. Mertsj

|dw:1375671659091:dw|

33. nikakuz

270?

34. Mertsj

yes. so the x value is 0 at 90, 270, 450, 630...

35. nikakuz

thank you soo much i just have one more

36. Mertsj

Or at -90, -270, -450...

37. nikakuz

same but tangent function

38. Mertsj

Do you know the definition of tangent?

39. nikakuz

umm no

40. Mertsj

tangent is equal to sin over cos Have you ever heard that?

41. nikakuz

i think ive heard it

42. Mertsj

$\tan x=\frac{ \sin x}{\cos x}$

43. Mertsj

The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0

44. nikakuz

ok so then wht

45. Mertsj

Are you trying to answer this question: Give 5 angles who tangent is 0?

46. nikakuz

the question is name five x values for which the tangent function equals to 0

47. Mertsj

Could you answer this question: Name five x values for which the sine function equals to 0?

48. nikakuz

yeah we already did that one

49. Mertsj

So did you read this post which I made a few moments ago: "The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0"

50. nikakuz

yeah i read it but i don't understand

51. Mertsj

The sin of 180 degrees is 0. Therefore the tangent of 180 degrees is also 0 The sin of 0 degrees is 0. Therefore the tangent of 0 degrees is also 0 The sin of 360 degrees is 0. Therefore the tangent of 360 degrees is also 0 The sin of 540 degrees is 0. Therefore the tangent of 540 degrees is also 0.

52. nikakuz

so my answer would be exactly the same as the sine one?

53. Mertsj

Let's make sure you understand this.

54. Mertsj

What is the sin of 180 degrees?

55. nikakuz

0

56. Mertsj

What is the cosine of 180 degrees?

57. Mertsj

$\tan 180^{o}=\frac{\sin 180^{o}}{\cos 180^{o}}=\frac{0}{-1}=0$

58. Mertsj

I guess you've gone. Good luck.

59. nikakuz

yeah i get it thank you soo much!!!!