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In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting ... more
Dolbear’s law states the relationship between the air temperature and the rate at which crickets chirp. It was formulated by Amos ... more
Landauer’s principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that “any ... more
An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... more
Dolbear’s law states the relationship between the air temperature and the rate at which crickets chirp. It was formulated by Amos ... 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
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/
Heat transfer describes the exchange of thermal energy, between physical systems depending on the temperature and pressure, by dissipating heat. The heat ... more
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more
A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... 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.