# Given the parametric equations #x=acos theta# and #y=b sin theta#. What is the bounded area?

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I got #-abpi# which is negative and clearly incorrect. What did I do wrong?

I got

The sign is wrong as the parametric equations trace out in an anti-clockwise direction which will give a negative area,

The area in parametric coordinates is given by:

As we trace out in clockwise direction.

Now, we have parametric equations:

And these equations trace out in an anti-clockwise direction and so we must take account that; So the area of the ellipse is given by:

Using the identity:

Give us:

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The bounded area enclosed by the curve described by the parametric equations (x = a\cos(\theta)) and (y = b\sin(\theta)) is a portion of the ellipse defined by those equations. The area can be calculated using the formula for the area of an ellipse, which is (A = \pi \times \text{{semi-major axis}} \times \text{{semi-minor axis}}), where the semi-major axis is (a) and the semi-minor axis is (b).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find a polar equation of the form #r=f(theta)# for the curve represented by the cartesian equation #x = 3#?
- What is the area bounded by the the inside of polar curve #1+cos theta# and outside the polar curve #r(1+cos theta)=1#?
- What is the area enclosed by #r=2cos((2theta)/3+(5pi)/3)+4sin(theta/2+pi/4) -theta# between #theta in [0,pi]#?
- What is the slope of the polar curve #f(theta) = theta - sectheta+thetasin^3theta # at #theta = (7pi)/12#?
- What is the distance between the following polar coordinates?: # (2,(pi)/8), (7,(3pi)/8) #

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