Help with solving parametric equation

  • #1
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0

Homework Statement


Consider the following parametric curve:

x=5cos^7(t)

y=5sin^7(t)

Write it in cartesian form, giving your answer as an equation of the form F(x,y)=c for some function F and some constant c.

The Attempt at a Solution


[/B]
I know that sin^2(t)+cos^2(t) = 1 but I don't think this will be much help to figure this out and I am also unsure how I would find the constant

Any help would be much appreciated
 

Answers and Replies

  • #2
954
117
I know that sin^2(t)+cos^2(t) = 1 but I don't think this will be much help to figure this out
Why not? How are ##x## and ##y## related to ##\sin^2(t)## and ##\cos^2(t)##?
 
  • #3
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0
Why not? How are ##x## and ##y## related to ##\sin^2(t)## and ##\cos^2(t)##?
would that mean x^2+y^2 = 1

which would mean

(5cos^7(t))^2 +(5sin^7(t))^2 = 1


25cos^9(t) +25sin^9(t) = 1

But what would I do now?
 
  • #4
954
117
would that mean x^2+y^2 = 1
Nope, that is not correct. Try to express ##\sin^2(t)## in terms of ##y## and ##\cos^2(t)## in terms of ##x##.
 
  • #5
52
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Nope, that is not correct. Try to express ##\sin^2(t)## in terms of ##y## and ##\cos^2(t)## in terms of ##x##.
would that mean

y=1-cos^2(t)

x=1-sin^2(t)
 
  • #6
954
117
would that mean

y=1-cos^2(t)

x=1-sin^2(t)
No, why would you think that?
You already have ##x## and ##y## defined in your original post: ##x = 5 \cos^7(t)## and ##y = 5 \sin^7(t)##.
Can you manipulate ##x = 5 \cos^7(t)## to get ##\cos^2(t)## in terms of ##x##? And likewise for ##\sin^2(t)## in terms of ##y##.
 
  • #7
SammyS
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Homework Statement


Consider the following parametric curve:

x=5cos^7(t)

y=5sin^7(t)

Write it in cartesian form, giving your answer as an equation of the form F(x,y)=c for some function F and some constant c.

The Attempt at a Solution


[/B]
I know that sin^2(t)+cos^2(t) = 1 but I don't think this will be much help to figure this out and I am also unsure how I would find the constant

Any help would be much appreciated
To start: Solve
##x=5\cos^7(t) ##​
for ##\ \cos(t)\ .##
 
  • #8
52
0
To start: Solve
##x=5\cos^7(t) ##​
for ##\ \cos(t)\ .##
cos(t)=(x/5)^(7/2)

Is this correct?
 
  • #9
SammyS
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cos(t)=(x/5)^(7/2)

Is this correct?
No. The exponent is wrong.
 
  • #10
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No. The exponent is wrong.

cos(t)=(x/5)^(1/7)

What would i do now?
 
  • #11
SammyS
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cos(t)=(x/5)^(1/7)

What would i do now?
That's better.

Do similar for y.

Square each & add.
 
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  • #12
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That's better.

Do similar for y.

Square each & add.
Thanks I got the right answer now!
 

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