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

Since we know that

By plugging

Hence, the curve is the portion of the parabola

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

- 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.
- Plot the points obtained from step 1 on the Cartesian plane.
- 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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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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- How do you differentiate the following parametric equation: # x(t)=1/t, y(t)=1/(1-t^2) #?

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