# Help with solving parametric equation

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1. May 10, 2016

### 53Mark53

1. The problem statement, all variables and given/known data
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.

3. The attempt at a solution

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

2. May 10, 2016

### Fightfish

Why not? How are $x$ and $y$ related to $\sin^2(t)$ and $\cos^2(t)$?

3. May 10, 2016

### 53Mark53

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. May 10, 2016

### Fightfish

Nope, that is not correct. Try to express $\sin^2(t)$ in terms of $y$ and $\cos^2(t)$ in terms of $x$.

5. May 10, 2016

### 53Mark53

would that mean

y=1-cos^2(t)

x=1-sin^2(t)

6. May 10, 2016

### Fightfish

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. May 10, 2016

### SammyS

Staff Emeritus
To start: Solve
$x=5\cos^7(t)$​
for $\ \cos(t)\ .$

8. May 10, 2016

### 53Mark53

cos(t)=(x/5)^(7/2)

Is this correct?

9. May 10, 2016

### SammyS

Staff Emeritus
No. The exponent is wrong.

10. May 10, 2016

### 53Mark53

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

What would i do now?

11. May 10, 2016

### SammyS

Staff Emeritus
That's better.

Do similar for y.

12. May 10, 2016

### 53Mark53

Thanks I got the right answer now!