## love_to_love_you one year ago Write an equation for the translation of y = 2/x that has the given asymptotes. x = 4 and y = -8 Show all work

1. love_to_love_you

@zepdrix

2. jim_thompson5910

what is the vertical asymptote for y = 2/x ?

3. love_to_love_you

oh nvm I don't even have to do this problem. Could you help me with something else?

4. love_to_love_you

@jim_thompson5910

5. jim_thompson5910

sure

6. love_to_love_you

Okay so what I have to do is explain why for each problem. I have the answers already but I do not know the explanation.

7. jim_thompson5910

ok

8. love_to_love_you

a. If sin theta = sqrt 2/2, which could not be the value of theta? 225 degrees

9. jim_thompson5910

where is 225 degrees? which quadrant?

10. love_to_love_you

11. jim_thompson5910

yes, and sine is negative in Q3 and Q4

12. jim_thompson5910

so it's impossible for theta to be 225 degrees

13. love_to_love_you

ok

14. love_to_love_you

b. For which value of theta is tan theta equal to sin theta? 2pi

15. jim_thompson5910

I'm guessing you had a list of choices?

16. love_to_love_you

It's a problem. I have 2 problems. They have a and b parts to them

17. love_to_love_you

So what we have to do is explain why this is the correct answer/ show work.

18. jim_thompson5910

well tan(theta) is the same as sin(theta)/cos(theta) it's one of the many identities

19. jim_thompson5910

$\Large \tan(\theta) = \sin(\theta)$ $\Large \frac{\sin(\theta)}{\cos(\theta)} = \sin(\theta)$ $\Large \frac{\sin(\theta)}{\cos(\theta)}*{\color{red}{\frac{1}{\sin(\theta)}}} = \sin(\theta)*{\color{red}{\frac{1}{\sin(\theta)}}}$ $\Large \frac{\cancel{\sin(\theta)}}{\cos(\theta)}*{\color{black}{\frac{1}{\cancel{\sin(\theta)}}}} = \cancel{\sin(\theta)}*{\color{black}{\frac{1}{\cancel{\sin(\theta)}}}}$ $\Large \frac{1}{\cos(\theta)} = 1$ in step 3, I'm multiplying both sides by 1/sin(theta) since both sides have a sine that cancels making sense so far?

20. love_to_love_you

Yeah

21. love_to_love_you

so what happens next?

22. jim_thompson5910

multiply both sides by cos(theta) to get cos(theta) = 1 then you'll use arccosine to isolate theta

23. love_to_love_you

Idk how to use arccosine very well

24. jim_thompson5910

what kind of calculator do you have?

25. love_to_love_you

just an online graphing calc

26. jim_thompson5910

what's the link to it? so I can have a look

27. love_to_love_you

28. jim_thompson5910

I gotcha

29. jim_thompson5910

ok I'm going to use this calculator here http://web2.0calc.com/

30. love_to_love_you

ok

31. jim_thompson5910

click the "rad" button (next to "deg") to convert over to radian mode

32. jim_thompson5910

then type in "arccos(1)" without quotes http://web2.0calc.com/#arccos(1) what do you get?

33. love_to_love_you

cos^-1(1) = 0

34. love_to_love_you

and then there's a tiny 2 pi under it

35. love_to_love_you

@jim_thompson5910

36. jim_thompson5910

37. jim_thompson5910

so since theta = 0 is one answer, theta = 2pi is also an answer there are infinitely many other answers. They only want theta = 2pi for some reason

38. love_to_love_you

So that makes 2 pi the answer as well?

39. jim_thompson5910

yeah there are infinitely many answers, but the computer or teacher is only accepting 2pi

40. love_to_love_you

ok

41. love_to_love_you

I'm gonna try to figure out a for the next problem on my own but can you help me with b?

42. love_to_love_you

A man stands on his balcony, 140 feet above the ground. He looks at the ground, with his sight line forming an angle of 75 degrees with the building, and sees a bus stop. The function d = 140 sec theta models the distance from the man to any object given his angle of sight theta. How far is the bus stop from the man? Round your answer. 541 ft.

43. jim_thompson5910

140*sec(theta) = 140*(1/cos(theta)) plug in theta = 75 make sure you are in degree mode use this calculator if needed http://web2.0calc.com/

44. love_to_love_you

541

45. jim_thompson5910

yeah I'm getting 540.9184627208766586 which rounds to 541 (assuming you round to the nearest foot)

46. love_to_love_you

yeah i rounded

47. love_to_love_you

Thanks so much

48. jim_thompson5910

you're welcome