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# c4 cartesian equation help watch

1. idk how to do this question plz help

x=2cot(t)
y=2sin^2(t)

find y=f(x)

i got this far:

sin^2(t) + cos^2(t) = 1

y/2 = sin^2(t)

x^2/4 + 1 = 2/y
2. (Original post by awijdijwajiodji)
idk how to do this question plz help

x=2cot(t)
y=2sin^2(t)

find y=f(x)

i got this far:

sin^2(t) + cos^2(t) = 1

y/2 = sin^2(t)

x^2/4 + 1 = 2/y
If x=2cot t then x²=4cot²t and you can rearrange for cos²t using cot=cos/sin
3. (Original post by MR1999)
If x=2cot t then x²=4cot²t and you can rearrange for cos²t using cot=cos/sin
i did that
4. (Original post by awijdijwajiodji)
idk how to do this question plz help

x=2cot(t)
y=2sin^2(t)

find y=f(x)

i got this far:

sin^2(t) + cos^2(t) = 1

y/2 = sin^2(t)

x^2/4 + 1 = 2/y
You're done. Just rearrange for y
5. x=2cot(t)
y=2sin^2(t)

This means x=2cos(t)/sin(t) --> x^2 = 4cos^2(t) / sin^2(t).

Now play around and use the Pythagorean identity.
6. (Original post by thekidwhogames)
x=2cot(t)
y=2sin^2(t)

This means x=2cos(t)/sin(t) --> x^2 = 4cos^2(t) / sin^2(t).

Now play around and use the Pythagorean identity.
and how do i do that

thats literally all i was asking, you can even see ive got that far
7. bump
8. (Original post by awijdijwajiodji)
idk how to do this question plz help

x=2cot(t)
y=2sin^2(t)

find y=f(x)

i got this far:

sin^2(t) + cos^2(t) = 1

y/2 = sin^2(t)

x^2/4 + 1 = 2/y
You have to multiply by y then divide by (x^2/4+1) to get it in the form y=f(x)
9. (Original post by awijdijwajiodji)
and how do i do that

thats literally all i was asking, you can even see ive got that far
x=2cot(t)
y=2sin^2(t)

x = 2cos(t)/sin(t) --> x^2 = 4cos^2(t)/sin^2(T)

y=2sin^2(t) --> y/2 = sin^2(t) -- > cos^2(t) = 1-y/2 --> 4cos^2(t) = 4-2y.

So...?
10. (Original post by psc---maths)
You have to multiply by y then divide by (x^2/4+1) to get it in the form y=f(x)
where the hell did this +1 come from

i got y = 8/x^2 +2
11. (Original post by awijdijwajiodji)
x^2/4 + 1 = 2/y
Now just make the subject.
12. (Original post by awijdijwajiodji)
idk how to do this question plz help

x=2cot(t)
y=2sin^2(t)

find y=f(x)

i got this far:

sin^2(t) + cos^2(t) = 1

y/2 = sin^2(t)

x^2/4 + 1 = 2/y
You have this

2/y = x^2/4 + 1

Multiplying by y gives us

2 = yx^2/4 + y

Which factorises as

2 = y(x^2/4 + 1)

So we can divide by (x^2/4 +1) to find y in terms of x
13. (Original post by RDKGames)
Now just make the subject.
idk why i keep trying and ive got this

y=2/1+x^2/4

and then i times the top by 4 to get rid of the 4 so i get:

8/1+x^2
14. (Original post by awijdijwajiodji)
idk why i keep trying and ive got this

y=2/1+x^2/4

and then i times the top by 4 to get rid of the 4 so i get:

8/1+x^2
You forgot to multiply the 1 by 4
15. (Original post by awijdijwajiodji)
idk why i keep trying and ive got this

y=2/1+x^2/4

and then i times the top by 4 to get rid of the 4 so i get:

8/1+x^2
Pretty much correct, but that 1 turns into a 4 in the denominator. It doesnt stay.
16. (Original post by psc---maths)
You forgot to multiply the 1 by 4

why would i do that, i noticed that too but i cant figure out why i should do that
17. (Original post by awijdijwajiodji)
why would i do that, i noticed that too but i cant figure out why i should do that
y=2 / (x^2/4 1)

That is

y=(2 / (x^2/4 1)) * (4 / 4) (#)

Now,

2*4 =8

And

(X^2/4 1) * 4 = 4x^2/4 4 = x^2 4

So, from (#)

y=8 / (x^2 4)

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