Question

INSTANT FAN MEDAL OR SNAPCHAT ;)
Find the corresponding rectangular equation represented by the parametric equations x = 1 + sec θ and y = 1 + tan θ by eliminating the parameter.

Answer 1

I solved for theta obviously, but I'm not sure how to simplify that further. Is there an identity I should be using?

Answer 2

these are the options http://puu.sh/oGsbP/b09533b4d2.png

Answer 3

\[x=1+\sec \theta--->\sec \theta=x-1--->\frac{ 1 }{ \cos \theta}=x-1--->\cos \theta=\frac{ 1 }{ x-1}\]

Answer 4

\[y=1+\tan \theta--->y=1+\frac{ \sin \theta }{ \cos \theta}--->(y-1)\cos \theta=\sin\]

Answer 5

Plug costheta into that equation

Answer 6

I would square one of the equations given (you use Pythagorean identity )
it should be easy to write in terms of x and y then

Answer 7

@freckles @nfcfox that makes it a lot simpler, thank you guys so much, i will update further with solution

Answer 8

are u k12

Answer 9

\[\sin^2\theta+\cos^2\theta=1---> ((y-1)(\frac{ 1 }{ x-1}))^2+(1/(x-1))^2=1\]

Answer 10

@czesc what's your sc

Answer 11

@nfcfox once i finish this assignment I'll send it to you privately so i dont get a billion adds

Answer 12

@czesc ok

Answer 13

btw what'd you get for the final rectangular equation @nfcfox

Answer 14

in terms of these options: http://puu.sh/oGsbP/b09533b4d2.png
@nfcfox

because I can't get anything like that lol

Answer 15

hey @czesc this is what I did
\[x=1+\sec(\theta) \\ \text{ square both sides } \\ x^2=(1+\sec(\theta))^2 \\ x^2=1+2 \sec(\theta)+\sec^2(\theta) \\ x^2=1+2 \sec(\theta)+1+\tan^2(\theta) \text{ by pythagorean identity } \\ x^2=2 +2 \sec(\theta)+\tan^2(\theta) \text{ adding like terms } \\ \\ \text{ now we can use our given equations to write } \\ \text{ the right hand side in terms of } x \text{ and } y\]

Answer 16

\[x=1+ \sec(\theta) \implies x-1=\sec(\theta) \\ y=1+\tan(\theta) \implies y-1=\tan(\theta)\]

Answer 17

plug in

Answer 18

@freckles that makes a lot of sense now, thank you so much

Answer 19

you will have to expand a little and get an equation equal to 0
to compare to your choices
but you shouldn't have too much more work to do from that above :)

Answer 20

@freckles yep you pretty much solved it lol

Answer 21

@freckles i wish i could give more than one medal :)

Answer 22

you can give the medal to the other guy
i have cookies at home that I can reward myself with

Answer 23

haha see you around thanks again!

Answer 24

HI!!

Answer 25

if it was me, i would cheat and get it quickly maybe

Answer 26

if you put \(\theta)=0\) you have the point \((2,1)\) on the graph
since you have choices, you can check