How do you sketch the curve with parametric equations #x = sin(t)#, #y=sin^2(t)# ?

Answer 1

Since we know that #-1 le sint le 1#, the curve is limited to #-1 le x le 1#.

By plugging #x=sint# into #y=sin^2t#, we have

#y=(sint)^2=x^2#.

Hence, the curve is the portion of the parabola #y=x^2# between #x=-1# and #x=1#, which looks like this:

I hope that this was helpful.

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Answer 2

To sketch the curve with parametric equations ( x = \sin(t) ) and ( y = \sin^2(t) ), follow these steps:

  1. Plot points: Choose a range of values for ( t ), such as ( t = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi ), and calculate corresponding ( x ) and ( y ) values using the given parametric equations.
  2. Plot the points obtained from step 1 on the Cartesian plane.
  3. Connect the points with a smooth curve to represent the graph of the parametric equations.

The resulting curve will resemble a portion of the graph of the function ( y = \sin^2(x) ), but it will be traced out in a particular manner as determined by the parameter ( t ).

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Answer from HIX Tutor

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.

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.

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