anonymous one year ago using complete sentences explain how to find the minimum value for each for each function and and determine which function has the smallest y value f(x) = 3x^2 + 12x + 16 And g(x) = 2sin (2x-pi) +4

1. anonymous

2. anonymous

@jim_thompson5910 I'm pretty sure the minimum point for f(x) is (-2, 4). Is that correct?

3. jim_thompson5910

yep the min for f is y = 4 when x = -2 ie the min f(x) = 4 occurs at the point (-2,4)

4. anonymous

Okay how to we find g(x)?

5. jim_thompson5910

when does sin(x) have a minimum?

6. anonymous

I don't know

7. jim_thompson5910

look at the unit circle what is the lowest point on it?

8. anonymous

(0, -1)?

9. jim_thompson5910

what is the corresponding angle

10. jim_thompson5910

I'll be right back in a few minutes

11. anonymous

(0, 1)? and okay

12. jim_thompson5910

I'm back no look at where it shows the angle theta

13. jim_thompson5910

what angle theta is where (0,-1) is located?

14. anonymous

I don't know what it is. I'm confused

15. jim_thompson5910

look at this http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png and tell me what the angle is

16. anonymous

I don't know I'm lost..

17. jim_thompson5910

do you see the 270 degrees?

18. anonymous

Yes

19. jim_thompson5910

so that's why sin(270 degrees) = -1 or sin(3pi/2 radians) = -1

20. jim_thompson5910

the min occurs when sin(x) = -1, ie when x = 3pi/2 so you have to determine when 2x-pi is equal to 3pi/2

21. jim_thompson5910

2x-pi = 3pi/2 what is x equal to?

22. anonymous

0?

23. jim_thompson5910

you should get x = 5pi/4

24. jim_thompson5910

I see a shortcut though

25. jim_thompson5910

they just want the min y value sin( anything ) has a min of -1 so 2sin (2x-pi) +4 turns into 2*(-1) +4 when you replace all of "sin..." with the smallest it can get, which is -1

26. anonymous

This is confusing to me.. I'm trying to understand it but it's a lot of info.. I'm not good with trigonometry

27. jim_thompson5910

2*(-1) +4 turns into 2, so this is the smallest that g(x) can get

28. jim_thompson5910

notice on the wavy graph, the lowest points have a y coordinate of y = 2

29. anonymous

Yea I noticed that. So y=2 but what is x? Do we need to know x?

30. jim_thompson5910

they just want to know the smallest output of the function

31. anonymous

Okay. So g(x) has the smallest minimum?

32. jim_thompson5910

yes

33. jim_thompson5910

and you can see that on your graph you posted

34. anonymous

Yeah I see that now haha. Do you mind helping with one more?

35. jim_thompson5910

alright

36. anonymous

Prove: $\sin \theta-\sin \theta \times \cos^2 \theta = \sin^3 \theta$

37. jim_thompson5910

hint: factor out sin(theta)

38. jim_thompson5910

only alter the left side do not change the right side

39. anonymous

So it would be $\cos^2 \theta = \sin^3 \theta?$

40. jim_thompson5910

you should have $\Large \sin(\theta)\left(1-\cos^2(\theta)\right) = \sin^3(\theta)$

41. jim_thompson5910

then try to do something with the 1-sin^2

42. anonymous

How would you get 1-sin^2?

43. jim_thompson5910

oops

44. jim_thompson5910

I meant 1-cos^2

45. anonymous

Would you multiply |dw:1433476582158:dw|

46. jim_thompson5910

nope

47. jim_thompson5910

there's an identity you use for 1-cos^2

48. jim_thompson5910

hint: sin^2 + cos^2 = 1

49. anonymous

So 1-cos^2 would become sin^2

50. jim_thompson5910

yep

51. anonymous

Thank you so much

52. jim_thompson5910

you're welcome

53. anonymous

Wait how did you get the 1 again?