Rotating a Parabola: 30o Anti-Clockwise About Origin

In summary, a parabola is a symmetrical curve formed by the intersection of a cone and a plane. Rotating a parabola means changing its position on a plane by turning it around a fixed origin point. Clockwise rotation is in the direction of clock hands, while anti-clockwise rotation is in the opposite direction. The rotation angle of 30 degrees specifies the amount and direction of rotation for a parabola, but any angle can be used. The origin for a parabola is the point (0,0) on a coordinate plane, which remains fixed while the rest of the parabola is rotated around it.
  • #1
squenshl
479
4
The parabola y = x2 is rotated anti-clockwise about the origin through the angle 30o. What is the new equation of the new curve (relative to the standard basis)?
 
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  • #2
If you have a point (x,x2) and you rotate it by 30 degrees around the origin what does it become?
 
  • #3
And you can rotate a point (x,y) through an angle [itex]\theta[/itex] about the origin by the matrix multiplication
[tex]\begin{bmatrix}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta)\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}[/tex].
 

FAQ: Rotating a Parabola: 30o Anti-Clockwise About Origin

What is a parabola?

A parabola is a type of mathematical curve that is shaped like an arch. It is a symmetrical curve that can be formed by the intersection of a cone and a plane.

What does it mean to rotate a parabola?

Rotating a parabola means changing its position on a plane by turning it around a fixed point, known as the origin. This changes the orientation of the parabola without altering its shape.

What is the difference between clockwise and anti-clockwise rotation?

Clockwise rotation is when an object is turned in the direction that clock hands move, from left to right. Anti-clockwise rotation is the opposite direction, from right to left.

Why is the rotation angle for this parabola specified as 30 degrees?

The rotation angle of 30 degrees specifies how much the parabola will be turned in a specific direction. It is an arbitrary value chosen for this example, but any angle can be used to rotate a parabola.

What is the origin for a parabola?

The origin for a parabola is the point (0,0) on a coordinate plane where the x and y axes intersect. When rotating a parabola, the origin is the point that remains fixed while the rest of the parabola is turned around it.

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