To analyze the given parametric equations:
- \( x = 2 \cos(t) \)
- \( y = \sin(t) \)
we can evaluate the statements provided:
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The parameter is x and the curve contains the points \( y = \sin(t) \): While \( y \) is indeed defined as \( \sin(t) \), \( x \) is not the parameter.
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The parameter is x and the curve contains the points \( y = \sin(t) \): Similar to statement 1, \( x \) is not the parameter.
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The parameter is y and the curve contains the points \( x = 2 \cos(t) \): This is incorrect since \( y \) is not the parameter.
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The parameter is y and the curve contains the points \( x = 2 \cos(t) \): Again, \( y \) is not the parameter.
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The parameter is t and the curve contains the set of points \( (2 \cos(t), \sin(t)) \): This statement is correct. Here, \( t \) is the parameter and it shows the points described by the parametric equations.
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The parameter is t and the curve contains the points \( ( \sin(t), 2 \cos(t) ) \): This is incorrect because the curve is given by \( (2 \cos(t), \sin(t)) \), not the reverse.
Therefore, the best statement that describes the curve is:
The parameter is t and the curve contains the set of points \( (2 \cos(t), \sin(t)) \).