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• Alan
Lv 7
2 months ago

Which interval part?

(For The original parametric equation that θ is between 0 and 2pi

or Are looking to restrict the resultant the rectangular equation?

that θ is between 0 and 2pi

However, that does really matter since the graph is repeats itself.

Going from 2pi to 4pi gives you the same graph over again.

Going from 4pi to 6pi gives you the same graph over again

and so on

Limiting the domain to 0 to 2pi just makes you complete the

graph once.   If you don't restrict the range, you just

trace over the same graph over and over again.

Sine and cosine are periodic function which repeat with a period of 2 pi

Also, there are no θ terms which are not sine and cosine.

The resultant cartesian equation range and domain are restricted

but you don't need to define it.

(x-2)^2/9 + (y+1)^2/4 = 1

The above equation restricts the cartesian range all by itself.

This is an equation of an ellipse

This is the equation

of an ellipse centered at

(2,-1) with semi-major axis of 3  and semi-minor axis of 2

focal length c = sqrt(5)

You don't have to define a range restriction unless you are using it to graph

in a tool.

• 2 months ago

sin(t) and cos(t) are bounded by -1 and 1

3 * (-1) + 2 < x < 3 * 1 + 2

-3 + 2 < x < 3 + 2

-1 < x < 5

2 * (-1) - 1 < y < 2 * 1 - 1

-2 - 1 < y < 2 - 1

-3 < y < 1

EDIT

Rather, it should be -1 </= x </= 5 and -3 </= y </= 1, with </= being less than or equal to