Write an equation for the translation of y = 2/x that has the given asymptotes.
x = 4 and y = -8
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- love_to_love_you

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- love_to_love_you

@zepdrix

- jim_thompson5910

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

- love_to_love_you

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

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## More answers

- love_to_love_you

@jim_thompson5910

- jim_thompson5910

sure

- 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.

- jim_thompson5910

ok

- love_to_love_you

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

- jim_thompson5910

where is 225 degrees? which quadrant?

- love_to_love_you

Um is it quadrant 3?

- jim_thompson5910

yes, and sine is negative in Q3 and Q4

- jim_thompson5910

so it's impossible for theta to be 225 degrees

- love_to_love_you

ok

- love_to_love_you

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

- jim_thompson5910

I'm guessing you had a list of choices?

- love_to_love_you

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

- love_to_love_you

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

- jim_thompson5910

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

- 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?

- love_to_love_you

Yeah

- love_to_love_you

so what happens next?

- jim_thompson5910

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

- love_to_love_you

Idk how to use arccosine very well

- jim_thompson5910

what kind of calculator do you have?

- love_to_love_you

just an online graphing calc

- jim_thompson5910

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

- love_to_love_you

it's a download from my school

- jim_thompson5910

I gotcha

- jim_thompson5910

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

- love_to_love_you

ok

- jim_thompson5910

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

- jim_thompson5910

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

- love_to_love_you

cos^-1(1) = 0

- love_to_love_you

and then there's a tiny 2 pi under it

- love_to_love_you

@jim_thompson5910

- jim_thompson5910

correct, so 0 radians is one answer
notice how 2pi radians and 0 radians are coterminal angles

- 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

- love_to_love_you

So that makes 2 pi the answer as well?

- jim_thompson5910

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

- love_to_love_you

ok

- 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?

- 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.

- 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/

- love_to_love_you

541

- jim_thompson5910

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

- love_to_love_you

yeah i rounded

- love_to_love_you

Thanks so much

- jim_thompson5910

you're welcome

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