Cuanto es 3 centenas -200
2 answers:
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The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is which is an ellipse.
For given question,
We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.
We need to convert given parametric equations to a rectangular equation and sketch the curve.
Given parametric equations can be written as,
x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.
We know that the trigonometric identity,
sin²t + cos²t = 1
⇒ (x/2)² + (- y/3)² = 1
⇒
This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.
The rectangular equation is
The graph of the rectangular equation is as shown below.
Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is which is an ellipse.
Learn more about the parametric equations here:
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Answer: The correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.
Explanation:
From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).
It means if the point is P(x,y) then after transformation it will be P'(y,x).
If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.
If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
Hence, the correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.