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In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center. ... more
In geometry and complex analysis, a Möbius transformation of the plane is a rational function of one complex variable. A Möbius transformation can be ... more
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). Altitude of a triangle is a line ... more
Parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped. The area enclosed between a parabola and a chord is two-thirds ... more
The exsphere of a face of a regular tetrahedron is the sphere outside the tetrahedron which touches the face and the planes defined by extending the ... more
Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of ... more
In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed ... 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/
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
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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.