Question

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

Show all work

Answer 1

@zepdrix

Answer 2

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

Answer 3

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

Answer 4

@jim_thompson5910

Answer 5

sure

Answer 6

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.

Answer 7

ok

Answer 8

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

Answer 9

where is 225 degrees? which quadrant?

Answer 10

Um is it quadrant 3?

Answer 11

yes, and sine is negative in Q3 and Q4

Answer 12

so it's impossible for theta to be 225 degrees

Answer 13

ok

Answer 14

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

Answer 15

I'm guessing you had a list of choices?

Answer 16

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

Answer 17

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

Answer 18

well tan(theta) is the same as sin(theta)/cos(theta)

it's one of the many identities

Answer 19

\[\Large \tan(\theta) = \sin(\theta)\]

\[\Large \frac{\sin(\theta)}{\cos(\theta)} = \sin(\theta)\]

\[\Large \frac{\sin(\theta)}{\cos(\theta)}*{\color{red}{\frac{1}{\sin(\theta)}}} = \sin(\theta)*{\color{red}{\frac{1}{\sin(\theta)}}}\]

\[\Large \frac{\cancel{\sin(\theta)}}{\cos(\theta)}*{\color{black}{\frac{1}{\cancel{\sin(\theta)}}}} = \cancel{\sin(\theta)}*{\color{black}{\frac{1}{\cancel{\sin(\theta)}}}}\]

\[\Large \frac{1}{\cos(\theta)} = 1\]

in step 3, I'm multiplying both sides by 1/sin(theta) since both sides have a sine that cancels

making sense so far?

Answer 20

Yeah

Answer 21

so what happens next?

Answer 22

multiply both sides by cos(theta) to get

cos(theta) = 1

then you'll use arccosine to isolate theta

Answer 23

Idk how to use arccosine very well

Answer 24

what kind of calculator do you have?

Answer 25

just an online graphing calc

Answer 26

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

Answer 27

it's a download from my school

Answer 28

I gotcha

Answer 29

ok I'm going to use this calculator here

http://web2.0calc.com/

Answer 30

ok

Answer 31

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

Answer 32

then type in "arccos(1)" without quotes

http://web2.0calc.com/#arccos(1)

what do you get?

Answer 33

cos^-1(1) = 0

Answer 34

and then there's a tiny 2 pi under it

Answer 35

@jim_thompson5910

Answer 36

correct, so 0 radians is one answer

notice how 2pi radians and 0 radians are coterminal angles

Answer 37

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

Answer 38

So that makes 2 pi the answer as well?

Answer 39

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

Answer 40

ok

Answer 41

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

Answer 42

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.

Answer 43

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/

Answer 44

541

Answer 45

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

Answer 46

yeah i rounded

Answer 47

Thanks so much

Answer 48

you're welcome