1/2 yearly question marked wrong.....i swear im right.... (1 Viewer)

[dawso]

ok, question is:

the parametric equations are given by:
x=a sin t y= sec t (where a is a constant)

find the cartesian equation of this equation.....

 

[acmilan]

This is my go at it:

x=a sin t
x² = a²sin²t
sin²t = x²/a²
cos²t = 1 - x²/a²

y= sec t
y² = sec²t
y² = 1/cos²t
y² = 1/(1 - x²/a²)
y² = 1/((a² - x²)/a²)
y² = a²/(a² - x²)

 

[dawso]

yeah, thats not wat i got, but it is a solution... (the one the teacher got)

i wanna see if anyone does wat i did, if not, ill post it up and u can tell me wat ya think...

 

[Eagles]

This is my go at it:

x=a sin t
x² = a²sin²t
sin²t = x²/a²
cos²t = 1 - x²/a²

y= sec t
y² = sec²t
y² = 1/cos²t
y² = 1/(1 - x²/a²)
y² = 1/((a² - x²)/a²)
y² = a²/(a² - x²)

that seems to follow logic, what did you do?

 

[dawso]

yeha, my solution is not very nice, but it does everythin required (onli in form of x + y) with no parameters....

x=a sin t

x
- = sin t
a


t = sin ^ -1 (x/a)

therefore

y = sec (sin ^ -1 (x/a))

as i said, not very elegent, but its right isnt it?? and alot shorter...

 

[Ogden_Nash]

Hmm, what if |x/a| > 1? The inverse sine is not defined for this.

 

[Xayma]

dawso: it is correct but isn't simplified I would go the next step to simplify it.

Ogden_Nash: x=asin t
x/a=sin t
∴
|x/a|≤1

 

[dawso]

yeah i realised that, if i had to use it in a question with more steps, then it would be best 2 simplify it, but its still the cartesian equation aye. shud get the marks

 

[Vampire]

they'll give you the marks man, dont worry about it

 

[rabdog]

im pretty sure he didnt get the marks for it...
btw vampire ur little display picture, my friend found that scene from family guy really funny and he sent it to me.. it wasnt that funny.. lol.