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In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed ... more
Distance is a numerical description of how far apart objects are. In analytic geometry, the distance between two points of the xy-plane can be found using ... more
Distance is a numerical description of how far apart objects are. In analytic geometry, the distance between two points of the xyz-plane in three-space, ... more
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most ... more
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most ... more
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most ... more
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. ... more
In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more
Nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet) has several ... more
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
... more
Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more
The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed ... more
In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates. the polar coordinate system is a two-dimensional coordinate system in ... more
The general equation for a circle with a center not necessary at the pole, gives the length of the radius of the circle.
The polar coordinate system
... more
In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more
Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more
A tacnode (also called a point of osculation or double cusp) is a kind of singular point of a curve. It is defined as a point where two (or more) ... more
The conchoid(s) of de Sluze is a family of plane curves. In Cartesian coordinates, the curves satisfy an implicit equation. They are rational, circular, ... more
In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more
In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more
A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more
A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more
Pell’s equation is a Diophantine equation (a polynomial equation in two or more unknowns ).
In Cartesian coordinates, the equation has the form
... more
A circle can be defined as the curve traced out by a point that moves so that its distance from a given point is constant. In an x–y Cartesian coordinate ... more
A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more
A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more
To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.
Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:
To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get
While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.
Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point
For x axis:
For y axis:
The coordinates of the character on the rotated map will be (-1.109, 5.725)
Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/
The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more
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In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.