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Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates ( x, y) with respect to the ...
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
Line graphs can be used to show how something changes over time. They have an x-axis (horizontal) and a y-axis (vertical). Usually, the x-axis has numbers for the time period, and the y-axis has numbers for what is being measured. Line graphs can be used when you're plotting data that has peaks (ups) and valleys (downs), or that was collected ...
When viewed at a position along the positive z-axis, the ¼ turn from the positive x-to the positive y-axis is counter-clockwise. For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise. Interchanging the labels of any two axes reverses the handedness.
Bar graphs can be used to show how something changes over time or to compare items. They have an x-axis (horizontal) and a y-axis (vertical). Typically, the x-axis has numbers for the time period or what is being measured, and the y-axis has numbers for the amount of stuff being measured. Bar graphs are good when you're plotting data that spans ...
For example, in the plane, if Cartesian coordinates (x, y) and polar coordinates (r, θ) have the same origin, and the polar axis is the positive x axis, then the coordinate transformation from polar to Cartesian coordinates is given by x = r cosθ and y = r sinθ.
Bar graphs have an x-axis and a y-axis. In most bar graphs, like the one above, the x-axis runs horizontally (flat). Sometimes bar graphs are made so that the bars are sidewise like in the graph below. Then the x-axis has numbers representing different time periods or names of things being compared. In these graphs, the x-axis has names of states.