Find the area of the graph enclosed by the parametric equations,

y = 6 cos(t) sin(t)

x= 6 cos^2(t)

Thus far I did some algebra and came up with 6x^2+6y^2= 36y, but am stuck after that.

Thank you!

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- Dec 16th 2013, 12:00 PMorangeParametric equations?
Find the area of the graph enclosed by the parametric equations,

y = 6 cos(t) sin(t)

x= 6 cos^2(t)

Thus far I did some algebra and came up with 6x^2+6y^2= 36y, but am stuck after that.

Thank you! - Dec 16th 2013, 12:10 PMPlatoRe: Parametric equations?
- Dec 16th 2013, 12:44 PMromsekRe: Parametric equations?
Did you plot the curve? The answer is pretty obvious if you do.

To do it formally though

dropping the t for convenience

so find the area under and double it to include the area under the

This will all be much clearer if you plot these functions.

As another trickier way of doing this

This is immediately recognized as a circle of radius 3 centered at (3,0).

It's area is - Dec 16th 2013, 01:06 PMSorobanRe: Parametric equations?
Hello, orange!

Quote:

Find the area of the area enclosed by the parametric equations: .

Square both equations: .

Add: . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . .

. .

. . . .

This is a circle with radius 3.

- Dec 16th 2013, 04:18 PMorangeRe: Parametric equations?
Thank you for all these wonderful explanations!